New Testament Isaiah
Isaiah is an "Old" Testament book of Prophecy, but like most of the other Hebrew prophetic books, it is about "New" Testament fulfillments, some up to now, many others yet in the future. It's the reason that they are so often quoted in the New Testament.
From Isaiah, describing the result of Christ's Crucifixion, for Him, and for all of humanity:
"52:14 As many were astonied at thee; his visage was so marred more than any man [see The Torturers Of Christ], and his form more than the sons of men: 52:15 So shall he sprinkle many nations; the kings shall shut their mouths at him: for that which had not been told them shall they see; and that which they had not heard shall they consider." (Isaiah 52:14-15 KJV)
"This day is this scripture fulfilled in your ears"
The "Old" Testament provides details of the life of Jesus Christ that sometimes provide more detail, before the fact, than the New Testament record does.
"53:1 Who hath believed our report? and to whom is the arm of the LORD revealed?
53:2 For he shall grow up before him as a tender plant, and as a root out of a dry ground: he hath no form nor comeliness; and when we shall see him, there is no beauty that we should desire him [see What Did Jesus Look Like?].
53:3 He is despised and rejected of men; a man of sorrows, and acquainted with grief: and we hid as it were our faces from him; he was despised, and we esteemed him not [see also Eloi, Eloi, Lama Sabachthani?].
53:4 Surely he hath borne our griefs, and carried our sorrows: yet we did esteem him stricken, smitten of God, and afflicted.
53:5 But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him; and with his stripes we are healed.
53:6 All we like sheep have gone astray [see Examples To The Flock]; we have turned every one to his own way; and the LORD hath laid on him the iniquity of us all. 53:7 He was oppressed, and he was afflicted, yet he opened not his mouth: he is brought as a lamb to the slaughter, and as a sheep before her shearers is dumb, so he openeth not his mouth. 53:8 He was taken from prison and from judgment: and who shall declare his generation? for he was cut off out of the land of the living: for the transgression of my people was he stricken. 53:9 And he made his grave with the wicked, and with the rich in his death; because he had done no violence, neither was any deceit in his mouth.
53:10 Yet it pleased the LORD to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin, he shall see his seed, he shall prolong his days, and the pleasure of the LORD shall prosper in his hand. 53:11 He shall see of the Travail of his soul [see Where Is Your Soul?], and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities.
53:12 Therefore will I divide him a portion with the great, and he shall divide the spoil with the strong; because he hath poured out his soul unto death [see What Happens When You Die?; also Through The Gates Of Hell]: and he was numbered with the transgressors; and he bare the sin of many, and made intercession for the transgressors." (Isaiah 53:1-12 KJV)
The Messiah Himself often quoted "Old" Testament prophecies (see Which Bible Did Jesus Use?), although the Truth that He spoke from it wasn't always appreciated (see The Messiah's Synagogue).
"4:16 And he came to Nazareth, where he had been brought up: and, as his custom was, he went into the synagogue on the sabbath day [see How To Be A True Christian - Lesson 4], and stood up for to read [see Aliyya and Haftara]. 4:17 And there was delivered unto him the book of the prophet Esaias. And when he had opened the book, he found the place where it was written, 4:18 The Spirit of the Lord is upon me, because he hath anointed me to preach the gospel to the poor; he hath sent me to heal the brokenhearted, to preach deliverance to the captives, and recovering of sight to the blind, to set at liberty them that are bruised,
4:19 To preach the acceptable year of the Lord.
4:20 And he closed the book, and he gave it again to the minister, and sat down. And the eyes of all them that were in the synagogue were fastened on him. 4:21 And he began to say unto them, This day is this scripture fulfilled in your ears." (Luke 4:16-21 KJV)
Fact Finder: Was King David also a prophet of the coming Messiah?
See David's Prophecies Of The Christ