1. Christ's priesthood
From among the people of Israel, designated as a kingdom of priests in Ex 19:6, the tribe of Levi was chosen by God for the service of the Tabernacle of the Testimony ( Num 1:50). Then, from among the tribe of Levi, the priests of the Old Covenant were consecrated with a rite of anointing (cf. Ex 29:1-7), giving them their special task: every high priest chosen among men is appointed to act on behalf of men in relation to God, to offer gifts and sacrifices for sins (Heb 5:1). As part of the Mosaic Law, by this priesthood a better hope [was] introduced (Heb 7:19), a shadow of the good things to come ( Heb 10:1); but of itself it [could] never, by the same sacrifices continually offered year after year, make perfect those who [drew] near (Heb 10:1).
The Levitical priesthood in some way prefigured among the chosen people the full realization of the priesthood in Jesus Christ—a priesthood linked not to genealogy, nor to temple sacrifices, nor to the Law, but only to God himself (cf. Heb 6:17-20 and 7:1ff). Hence Christ was designated by God a high priest after the order of Melchizedek (Heb 5:10); for by a single offering he has perfected for all time those who are sanctified (Heb 10:14). And truly the Word of God made flesh, in fulfilment of the messianic prophecies, redeemed all men and women by his death and resurrection, giving his own life in fulfilment of his priestly role. Hence this priesthood, which Christ himself describes in terms of consecration and mission (cf. Jn 10:1 ) , has a universal value: there is no “salvific action of God beyond the unique mediation of Christ." 
2. The priesthood of the apostles and in the apostolic succession
At the Last Supper Jesus made known his desire to have the apostles share in his priesthood, expressed as consecration and mission: As thou didst send me into the world, so I have sent them into the world. And for their sake I consecrate myself, that they may also be consecrated in truth (Jn 17:18-19). This participation became a reality at different moments throughout our Lord's ministry, which can be thought of a successive steps leading to the institution of Holy Orders: when he calls the apostles and forms them into a college (cf. Mk 3:13-19); when they receive instructions and are sent out to preach (cf. Lk 9:1-6); when they are given the power to forgive sins (cf Jn 20:22-23); when they are given a universal mission (cf. Mt 28:18-20); and the very special occasion when they are ordained to celebrate the Eucharist: do this in memory of me (1 Cor 11:24). And their apostolic mission “was fully confirmed on the day of Pentecost." 
During their life “they not only had helpers in their ministry, but also, in order that the mission assigned to them might continue after their death, they passed on to their immediate cooperators, as it were, in the form of a testament, the duty of confirming and finishing the work begun by themselves … and gave them the order that, when they should have died, other approved men would take up their ministry." In this way “bishops, therefore, with their helpers, the priests and deacons, have taken up the service of the community, presiding in place of God over the flock, whose shepherds they are, as teachers for doctrine, priests for sacred worship, and ministers for governing." 
2.1 Ordination liturgy
In the New Testament the apostolic ministry is transmitted through the imposition of hands accompanied by a prayer (cf. Acts 6:6; 1 Tim 4:14; and 5:22; 2 Tim 1:6). This is the practice found in the most ancient ordination rites, as seen in the Traditio Apostolica and the Statuta Ecclesiae Antiqua . Down through the ages, this essential nucleus, which forms the sacramental sign, has been enriched by complementary rites differing according to liturgical traditions. “In the Latin Church, the initial rites—presentation and election of the ordinand, instruction by the bishop, examination of the candidate, litany of the saints—attest that the choice of the candidate is made in keeping with the practice of the Church and prepare for the solemn act of consecration, after which several rites symbolically express and complete the mystery accomplished: for bishop and priest, an anointing with holy chrism, a sign of the special anointing of the Holy Spirit who makes their ministry fruitful; giving the book of the Gospels, the ring, the miter, and the crosier to the bishop as the sign of his apostolic mission to proclaim the Word of God, of his fidelity to the Church, the bride of Christ, and his office as shepherd of the Lord's flock; presentation to the priest of the paten and chalice, 'the offering of the holy people' which he is called to present to God; giving the book of the Gospels to the deacon who has just received the mission to proclaim the Gospel of Christ" (CCC , 1574)
2.2 Nature and effects of the orders received
Through the sacrament of Holy Orders a participation in the priesthood of Christ is conferred, stemming from the apostolic succession. The ministerial priesthood is distinct from the common priesthood of the faithful that comes from Baptism and Confirmation; “each is ordered one to another," but “they differ from one another in essence and not only in degree."  By the ministerial priesthood “priests are a sacramental representation of Jesus Christ, Head and Shepherd,"  enabling them to exercise Christ's authority in the pastoral functions of teaching, governing and acting in persona Christi in the exercise of their sacramental ministry.
The repraesentatio Christi Capitis is always preserved in the minister, whose soul has been sealed with the sacramental character, indelibly impressed on his soul at ordination. This character is the principal effect of the sacrament, and since it is a permanent reality, the orders conferred can neither be repeated nor eliminated nor conferred for a limited time. “It is true that someone validly ordained can, for grave reasons, be discharged from the obligations and functions linked to ordination, or can be forbidden to exercise them; but he cannot become a layman again in the strict sense" (CCC , 1583).
Ordination in each of its degrees confers “the grace of the Holy Spirit proper to this sacrament," which “is configuration to Christ as Priest, Teacher and Pastor, of whom the ordained is made a minister" (CCC , 1585). This ministry is as much a gift as a task, since the priestly order is received with a view to service to Christ and to the faithful, who in the Church make up his Mystical Body. Specifically for a bishop the gift received is “the Spirit of governing which you gave to your beloved Son, Jesus Christ, and which he, in turn, communicated to the holy apostles."  In the ordination of a priest, God is asked to bestow the gift of the Spirit so that the new priest “may be worthy to stand without reproach before your altar, to proclaim your kingdom, to carry out the ministry of your word of truth, to offer you spiritual gifts and sacrifices, to renew your people by the bath of rebirth."  While in the ordination of deacons, God is beseeched so that “strengthened by sacramental grace, in communion with the bishop and his group of priests, they may serve in the ministry of the liturgy, of the word, and of charity to the people of God." 
2.3 The degrees of the sacrament of Holy Orders
The diaconate, the priesthood and the episcopate are intimately related as grades of the one sacrament of Holy Orders, received successively and inclusively. At the same time they are distinguished according to the sacramental reality conferred and their corresponding functions in the Church.
The episcopate is “the fullness of the sacrament of Orders," called “in the Church's liturgical practice and in the language of the Fathers 'the high priesthood' or the supreme power of the sacred ministry."  Bishops are entrusted with “the service of the community, presiding in place of God over the flock, whose shepherds they are, as teachers for doctrine, priests for sacred worship, and ministers for governing."  They are successors of the apostles and in virtue of their ordination become members of the episcopal college, in hierarchical communion with the Pope, head of the college, and with the other members of the college. The bishops' principle task is that of headship, both in the universal Church and in presiding over the local Churches “as vicars and ambassadors of Christ, which they govern by their counsel, exhortations and example, and over and above all by their authority and sacred power."  “Among the principal duties of bishops, the preaching of the Gospel occupies a preeminent place. For bishops are preachers of the faith, who lead new disciples to Christ, and they are authentic teachers, that is, teachers endowed with the authority of Christ, who preach to the people entrusted to them the faith they must believe and put into practice;" “the bishops, teaching in communion with the Roman Pontiff, are to be respected by all as witnesses to divine and Catholic truth."  Finally, as administrators of the grace of the supreme priesthood, they guide with their authority the health-giving and fruitful administration of the sacraments. “They direct the conferring of baptism, by which a sharing in the royal priesthood of Christ is granted. They are the original ministers of confirmation, dispensers of sacred Orders and the moderators of penitential discipline, and they earnestly exhort and instruct their people to carry out with faith and reverence their part in the liturgy and especially in the holy sacrifice of the Mass." 
The priesthood has been instituted by God “so that its ministers by the sacred power of orders are able to offer sacrifice and to forgive sins; they perform their priestly office publicly for men in the name of Christ."  “Their ministry has been handed down, in a lesser degree, but established in the order of the priesthood they can be co-workers of the episcopal order for the proper fulfillment of the apostolic mission."  They share “the authority by which Christ builds up, sanctifies and rules his Body," and through the sacramental order they have received, “they are signed with a special character and are conformed to Christ the Priest in such a way that they can act in the person of Christ the Head."  They “constitute one priesthood with their bishop [dedicated to] a diversity of duties,"  and carry out their mission in immediate contact with the people. More specifically, “priests, as co-workers with their bishops, have the primary duty of proclaiming the Gospel of God to all. In this way they fulfill the command of the Lord: 'Going therefore into the whole world, preach the Gospel to every creature' (Mk 16:15)."  “They exercise their sacred function especially in the Eucharistic worship; there, acting in the person of Christ and proclaiming his Mystery, they unite the prayers of the faithful with the sacrifice of their Head and renew and apply in the sacrifice of the Mass, until the coming of the Lord, the unique sacrifice of the New Testament, namely that of Christ offering Himself once for all a spotless Victim to the Father (cf. Heb 9:11-28)."  This function is united with “the ministry of reconciliation and comfort" for “the sick and the sinners." As true shepherds, they exercise “within the limits of their authority the function of Christ as Shepherd and Head, they gather together God's family as a brotherhood all of one mind, and lead them in the Spirit, through Christ, to God the Father." 
Deacons are the lowest grade of the hierarchy of orders. They are ordained “not unto the priesthood, but unto a ministry of service," which they exercise as repraesentatio Christi Servi Their role is “to administer baptism solemnly, to be custodian and dispenser of the Eucharist, to assist at and bless marriages in the name of the Church, to bring Viaticum to the dying, to read the Sacred Scripture to the faithful, to instruct and exhort the people, to preside over the worship and prayer of the faithful, to administer sacramentals, to officiate at funeral and burial services." 
3. Minister and Subject
The administration of all three grades of Holy Orders is reserved exclusively to the bishop. In the New Testament only the apostles conferred it and, “since the sacrament of Holy Orders is the sacrament of the apostolic ministry, it is for the bishops as the successors of the apostles to hand on the 'gift of the Spirit,' the 'apostolic line,'"(CCC , 1576), which has been preserved through the centuries in the ordained ministry.
An explicit papal mandate is needed for licit Episcopal ordination in the Latin rite (cf. Code of Canon Law , 1013). In the Eastern Churches this is reserved to the Roman Pontiff, the Patriarch or the Metropolitan, and it is always illicit if there is no legitimate mandate. In the case of the ordination of priests and deacons, the person ordaining must be their own bishop unless they have dimissorial letters from the competent authority (cf. Code of Canon Law , 1015-1016). If the ordination is to take place outside their own circumscription they need the venia of the diocesan bishop (cf. Code of Canon Law, 1017).
For an ordination in all three grades to be valid, the candidate must be a baptized male. Christ ordained only men in spite of the fact that among his followers there were also women who on various occasions showed greater fidelity.
Our Lord's example here has been the norm of the Church throughout her life and cannot be considered merely circumstantial, since the apostles followed this practice and ordained only on men even when the Church spread to areas where women priests would have caused no surprise. The Fathers of the Church followed the practice of the apostles, aware that it was a binding tradition, laid down in synod degrees. Consequently the Church “does not consider herself authorized to admit women to priestly ordination." 
For an ordination to be legitimate and fully fruitful it is also necessary that the candidate have a truly supernatural vocation and that this is confirmed by the invitation of the competent authority (the “calling from the hierarchy"). The Latin Church has the law of ecclesiastical celibacy for the three grades. “Indeed, it is not demanded by the very nature of the priesthood,"  but it “has a many-faceted suitability for the priesthood." Through it clerics share in the celibacy that Christ adopted in order to carry out his mission “They adhere to him more easily with an undivided heart, they dedicate themselves more freely in him and through him to the service of God and men.“ With the total surrender of their lives to the mission they have been given, those ordained “evoke the mysterious marriage established by Christ … in which the Church has Christ as her only Spouse. They give, moreover, a living sign of the world to come, by a faith and charity already made present, in which the children of the resurrection neither marry nor take wives."  This does not oblige permanent deacons, nor does it oblige deacons and priests of the Eastern Churches. Finally in order to be ordained specific internal and external dispositions are needed, together with the required age and necessary learning, the preliminary requirements for ordination and the absence of any impediments and irregularities (cf. CCC , 1029-1042). Special conditions exist for episcopal ordination candidates to ensure their suitability for their office (cf. Code of Canon Law , 378).
Catechism of the Catholic Church , 1533-1600
Second Vatican Council, Const. Lumen Gentium , 18-29; Decree: Presbyterorum Ordinis, 2: 4-6 and 15-17,
St Josemaria, Homily A Priest Forever , in In Love with the Church
 Congregation for the Doctrine of the Faith, Declaration Dominus Iesus , August 6, 2000, 14.
 Second Vatican Council, Const. Lumen Gentium , no. 19.
 Ibid., 20.
 Ibid., 10.
 John Paul II: Apost. Exhort. Pastores Dabo Vobis , March 25, 1992, 15,4.
 Roman Pontifical, Prayer of Consecration for Episcopal Ordination.
 Byzantine Rite, Prayer for Priestly Ordination.
 Second Vatican Council, Lumen Gentium , 29.
 Ibid., 21 .
 Ibid., 20 .
 Ibid., 27 .
 Ibid., 25.
 Ibid., 26.
 Second Vatican Council, Decree Presbyterorum Ordinis , 2.
 Second Vatican Council, Lumen Gentium , 28.
 Presbyterorum Ordinis , 4.
 Lumen Gentium , 28.
 Ibid., 29.
 John Paul II, Apostolic Letter, Ordinatio Sacerdotalis , May 22, 1994, 2.
 Presbyterorum Ordinis , 16.