"[We must consider] the conceptual and symbolic universe in which they moved. It will be necessary to examine the images and symbols inherited from the Old Testament or from Jewish culture, and the modifications and adaptations made by the evangelists and other writers of the New Testament. It is necessary to note also the new images and symbols that they present following traditional lines, and to notice the new meanings they give to old terms to enable them to express different realities, as well as the ways of indicating the existence of a theological meaning in passages which at first sight appear to be mere historical accounts. In this regard the Gospel writers do not invent a new style, but rather are influenced by the methods applied to the OT Scriptures in Rabbinic schools. In these schools, they commented on the ancient books, adapting them to the circumstances of the day and in accordance with the new demands of the day. In oral or written exposition, the commentary could take the form of Madras, which consisted in glossing an ancient narrative, amplifying its contents with new additions and adapting it step by step to the new message they wished to convey. It is also necessary to consider, in a more limited form, the use of already existing symbols that had been assimilated into the culture, separately or together, as appropriate. The writers could also take the main idea of a passage or verse and develop it into narrative form. With this material at their disposal, the Gospel writers sometimes allude to particular Old Testament passages, which at other times they use the many and varied prototypes and symbols that were being formed within the Jewish culture."To that extent the Old Testament was the primary and essential referent of the New Testament. Augustine recognized the importance for Christians of understanding the Old Testament, asserting that "[t]he New Testament is hidden in the Old, and the latter is revealed in the New" (Quaestionum in Heptateuchum libri Septem 2.73). The New Testament cannot be correctly interpreted without knowledge of the Old Testament and its conceptual, figurative, and symbolic universe.
There is continuity and discontinuity between the two Testaments. Some theological lines of the Old Testament have been adopted by the New Testament writers (seeing the latter as the expansion of the former). Others, however, have been either ignored or rejected. In any case, the authors of the New Testament interpreted and developed these texts with great liberty, sometimes regarding the Old Testament as not so much a fixed given as a literary resource.
As a religious group born from the womb of Judaism, Christianity and its basic book, the New Testament, are the formal heirs of all the theological riches of the Hebrew Bible. The essential points of this tradition were pointed out by R. Bultmann. I have also discussed these connection points in some of my own publications. Let me identify three.
1. Belief in a single personal God who transcends the world while maintaining continuous contact with it.
2. The sovereignty of God, whose salvific effects appear throughout human history, is manifested in this world.
3. The relationship between God and human beings is measured by obedience to the Torah or Law, manifested in the Scriptures and conceived in terms of covenant, a covenant by which the people promised to worship Yahweh as the only God and he, in turn, would protect, lead, and deliver his people. Participation in this covenant was confirmed by strict compliance with the Law. Consequently, Christianity was heir to a religion that made reference to a moral demand, perfectly articulated in clear commandments, though in the Gospels Jesus reduces the plurality of these, establishing a clear hierarchy, with just two at the top. The first is: "Hear, O Israel! The Lord our God is one Lord; and you shall love the Lord your God with all your heart, all your soul, and al your might" (Deut. 6:6). The second is, "You shall love your neighbors as yourself" (Lev. 19:18). There is no other commandment greater than these" (Mark 12:30–31)Along with these, New Testament Judaism also inherited the sense of guilt, sin, and expiation; the fulfillment of God's promises to Abraham and the kingdom of God; etc.
You can't study the New Testament without studying the Old Testament. It is an essential resource, one that must be within our reach as we study the texts of the New Testament.
*The above is taken with only slight modification from Antonio Piñero and Jesús Peláez, The Study of the New Testament: A Comprehensive Introduction, trans. David E. Orton and Paul Ellingworth, Tools for Biblical Studies 3 (Leiden: Deo, 2003), 213-215.