Please give me a study report about the virgin birth (Isaiah 7:14Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel.
See All...) and its fulfillment in the New Testament.

The virgin birth is the doctrinal term referring to Mary giving birth to Jesus by the power of the Holy Ghost and without having had any physical relations with any man. It is clearly taught in the New Testament records of the birth of Jesus.

Matthew 1:18Now the birth of Jesus Christ was on this wise: When as his mother Mary was espoused to Joseph, before they came together, she was found with child of the Holy Ghost.
See All... Now the birth of Jesus Christ was on this wise: When as his mother Mary was espoused to Joseph, before they came together, she was found with child of the Holy Ghost.

Luke 1:34-35 [34] Then said Mary unto the angel, How shall this be, seeing I know not a man? [35] And the angel answered and said unto her, The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee: therefore also that holy thing which shall be born of thee shall be called the Son of God.
See All... Then said Mary unto the angel, How shall this be, seeing I know not a man? And the angel answered and said unto her, The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee: therefore also that holy thing which shall be born of thee shall be called the Son of God.

This doctrine is important because it is the way that God became a man and in Jesus Christ became the God-man. According to the scriptures, in Jesus "the Word was made flesh, and dwelt among us" (John 1:14And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.
See All...). The mystery of godliness was that "God was manifest in the flesh" (1 Timothy 3:16And without controversy great is the mystery of godliness: God was manifest in the flesh, justified in the Spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory.
See All...). This is why the One who was born as Jesus Christ was also called "Emmanuel, which being interpreted is, God with us" (Matthew 1:23Behold, a virgin shall be with child, and shall bring forth a son, and they shall call his name Emmanuel, which being interpreted is, God with us.
See All...). He is both fully God and fully man. He has two natures--the human and the divine--in one person.

By being born and living as a man, Jesus came as the "second man" (1 Corinthians 15:47The first man is of the earth, earthy; the second man is the Lord from heaven.
See All...) and the "last Adam" (1 Corinthians 15:45And so it is written, The first man Adam was made a living soul; the last Adam was made a quickening spirit.
See All...). As such, all that was lost in the sin and fall of the first Adam will be restored in the last Adam (Romans 5:14-18 [14] Nevertheless death reigned from Adam to Moses, even over them that had not sinned after the similitude of Adam's transgression, who is the figure of him that was to come. [15] But not as the offence, so also is the free gift. For if through the offence of one many be dead, much more the grace of God, and the gift by grace, which is by one man, Jesus Christ, hath abounded unto many. [16] And not as it was by one that sinned, so is the gift: for the judgment was by one to condemnation, but the free gift is of many offences unto justification. [17] For if by one man's offence death reigned by one; much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ.) [18] Therefore as by the offence of one judgment came upon all men to condemnation; even so by the righteousness of one the free gift came upon all men unto justification of life.
See All...). He came in the "likeness of sinful flesh" so that He might condemn "sin in the flesh" (Romans 8:3For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh:
See All...). By being both God and man, He is able as God to provide an effective sacrifice for our sins (Hebrews 9:23-28 [23] It was therefore necessary that the patterns of things in the heavens should be purified with these; but the heavenly things themselves with better sacrifices than these. [24] For Christ is not entered into the holy places made with hands, which are the figures of the true; but into heaven itself, now to appear in the presence of God for us: [25] Nor yet that he should offer himself often, as the high priest entereth into the holy place every year with blood of others; [26] For then must he often have suffered since the foundation of the world: but now once in the end of the world hath he appeared to put away sin by the sacrifice of himself. [27] And as it is appointed unto men once to die, but after this the judgment: [28] So Christ was once offered to bear the sins of many; and unto them that look for him shall he appear the second time without sin unto salvation.
See All...) and as man to sympathize with our weaknesses and temptations (Hebrews 4:14-16 [14] Seeing then that we have a great high priest, that is passed into the heavens, Jesus the Son of God, let us hold fast our profession. [15] For we have not an high priest which cannot be touched with the feeling of our infirmities; but was in all points tempted like as we are, yet without sin. [16] Let us therefore come boldly unto the throne of grace, that we may obtain mercy, and find grace to help in time of need.
See All...).

The clearest prophecy of the virgin birth is in Isaiah 7:14Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel.
See All..., which states:

"Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel."

Here, a virgin is to bear a son and that son will be called Immanuel which means "God with us."  If the child is God with us and the mother is a virgin, we have a clear prophecy of the virgin birth.

However, there are other prophetic statements that certainly point to the virgin birth. Immediately after the fall of Adam and Eve, the Lord declared unto the serpent, "And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel" (Genesis 3:15And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel.
See All...). The woman is said to have a seed and her seed is to bruise the head of the serpent or devil. The seed of the woman is certainly Jesus Christ. But how is the virgin birth implied here? It is in the concept of the woman having a seed. In the Bible, the seed refers to the man's part in bringing forth a child--though seed can also refer simply to offspring (as in Leviticus 12:2Speak unto the children of Israel, saying, If a woman have conceived seed, and born a man child: then she shall be unclean seven days; according to the days of the separation for her infirmity shall she be unclean.
See All...). But here in Genesis 3:15And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel.
See All..., the One to come and bruise the serpent's head is specifically called the woman's seed. Clearly, the virgin birth is in mind.

Another possible reference to the virgin birth is in Jeremiah 31:22How long wilt thou go about, O thou backsliding daughter? for the LORD hath created a new thing in the earth, A woman shall compass a man.
See All..., which states, "How long wilt thou go about, O thou backsliding daughter? for the LORD hath created a new thing in the earth, A woman shall compass a man." The idea of a woman compassing a man is said to be a new thing in the earth created by the Lord. This must refer to much more than a natural birth and would match up with Jesus Christ being the woman's seed.

Isaiah 9:6For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.
See All... points to the dual nature of the Messiah:

Isaiah 9:6For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.
See All... For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.

Notice that the child is born. That is the natural way of things and points to the humanity of Christ. However, the son is given. Something given already exists. Here, that something is the Son and is called "The mighty God." He must be both God and man and His birth must take a form where the everlasting God can be born as a human child. That, of course, is the virgin birth.

As with any doctrine, there is much more that could be said. I just hope that this gives you a good introduction to the subject.