The first beast is introduced in chapter 13,
And the dragon stood on the shore of the sea. And I saw a beast coming out of the sea. He had ten horns and seven heads, with ten crowns on his horns, and on each head a blasphemous name. The beast I saw resembled a leopard, but had feet like those of a bear and a mouth like that of a lion. The dragon gave the beast his power and his throne and great authority. One of the heads of the beast seemed to have had a fatal wound, but the fatal wound had been healed. The whole world was astonished and followed the beast. Men worshiped the dragon because he had given authority to the beast, and they also worshiped the beast and asked, “Who is like the beast? Who can make war against him?”
Then I saw another beast, coming out of the earth. He had two horns like a lamb, but he spoke like a dragon. He exercised all the authority of the first beast on his behalf, and made the earth and its inhabitants worship the first beast, whose fatal wound had been healed. And he performed great and miraculous signs, even causing fire to come down from heaven to earth in full view of men. Because of the signs he was given power to do on behalf of the first beast, he deceived the inhabitants of the earth. He ordered them to set up an image in honor of the beast who was wounded by the sword and yet lived. He was given power to give breath to the image of the first beast, so that it could speak and cause all who refused to worship the image to be killed. He also forced everyone, small and great, rich and poor, free and slave, to receive a mark on his right hand or on his forehead, so that no one could buy or sell unless he had the mark, which is the name of the beast or the number of his name. This calls for wisdom. If anyone has insight, let him calculate the number of the beast, for it is man’s number. His number is 666.
What is less appreciated is that in this type of genre, an ancient style of writing called Apocalyptic writings, much of the imagery is well known and can fairly straightforwardly be interpreted. I cannot go into everything here so will sketch a few highlights. The first beast is said to  get its authority from the dragon,  resemble a leopard, a bear and a lion,  have 7 heads and 10 horns, we know also that  everyone will worship this beast and no one can defeat it in battle. I will suggest that when one examines this imagery, by looking at its use elsewhere in the same genre, one can get a reasonably accurate picture of what the author is getting at.
The first point  is fairly straightforward. The dragon, is identified as “the ancient serpent.” The allusion here is to the story of Adam and Eve in the first three chapters of Genesis; there the serpent is a crafty creature that tempts Adam and Eve to try to be like God and encourages them to disobey God’s commands. The imagery in  is also familiar, the picture comes from the book of Daniel,
Daniel said: “In my vision at night I looked, and there before me were the four winds of heaven churning up the great sea. Four great beasts, each different from the others, came up out of the sea. “The first was like a lion, and it had the wings of an eagle. I watched until its wings were torn off and it was lifted from the ground so that it stood on two feet like a man, and the heart of a man was given to it. “And there before me was a second beast, which looked like a bear. It was raised up on one of its sides, and it had three ribs in its mouth between its teeth. It was told, ‘Get up and eat your fill of flesh!’ “After that, I looked, and there before me was another beast, one that looked like a leopard. And on its back it had four wings like those of a bird. This beast had four heads, and it was given authority to rule.” After that, in my vision at night I looked, and there before me was a fourth beast–terrifying and frightening and very powerful. It had large iron teeth; it crushed and devoured its victims and trampled underfoot whatever was left. It was different from all the former beasts, and it had ten horns.
I, Daniel, was troubled in spirit, and the visions that passed through my mind disturbed me. I approached one of those standing there and asked him the true meaning of all this. So he told me and gave me the interpretation of these things: The four great beasts are four kingdoms that will rise from the earth. [Emphasis added]
This leaves  which gives us a more precise identification; this symbolism is again explained elsewhere in the scriptures, specifically in Revelation 17:9-14;
This calls for a mind with wisdom. The seven heads are seven hills on which the woman sits. They are also seven kings. Five have fallen, one is, the other has not yet come; but when he does come, he must remain for a little while. The beast who once was, and now is not, is an eighth king. He belongs to the seven and is going to his destruction. The ten horns you saw are ten kings who have not yet received a kingdom, but who for one hour will receive authority as kings along with the beast. They have one purpose and will give their power and authority to the beast. They will make war against the Lamb, but the Lamb will overcome them because he is Lord of lords and King of kings–and with him will be his called, chosen and faithful followers.
Second, the seven heads symbolise “seven kings. Five have fallen, one is, the other has not yet come; but when he does come, he must remain for a little while.” If one follows the order of Suetonius and other forms of apocalyptic literature such as The Orac Sibyl 5:12 and II Esd 12.15, the first king of Rome was Julius Caesar, the second was Augustus, the third Tiberius, the fourth Caligula, the fifth was Claudius, the sixth who “now is” would then be Nero Caesar, the seventh who “has not yet come” but who will “remain for a little while” would be Galba who reigned for seven months.
Interestingly, Nero was called “the beast” by some of his contemporaries. John AT Robinson notes that he established the emperor cult in Rome setting up a statute of himself; in his time the emperor and the empire were worshipped as Gods.
The first beast then was not some future anti-christ leading a coalition of nations that one sees in Hollywood movies, it refers to the Roman Empire represented in the person of Nero at the time of John’s writing.
This also sheds light of the infamous number of the beast. In Greek and Latin the letters and numbers are interchangeable; for this reason one can add up the letters of peoples names to get numerical figures that stand for their name. In Hebrew writings a system of Gematria developed (though it is also found in Greek and Roman writings) whereby a person would assign a numerical value to a word or phrase. Interestingly when the Greek word Nero Caesar is translated into Hebrew the system of Gematria yields the number 666. If one transliterates the Latin instead of the Greek one gets 616; not only then does Nero fit the picture given in the text and make a historically plausible candidate for the “number of the beast” but this account also explains why some manuscripts have 666 and others 616. In the first century, Greek was the international language of the Roman Empire and was native to much of the eastern empire. Latin, however, was the language of the Romans. If the beast was Nero then it makes sense that some communities would cite his name in Greek and others would use Latin.
These insights make it evident as to what the second beast of Revelation 13 refers to; the second beast has “two horns like a lamb, but he spoke like a dragon.” The lamb in Revelation refers to Christ; this is an institution that appears to speak on behalf of God but in fact tempts people into doing wrong. It exercises “all the authority of the first beast on his behalf, and made the earth and its inhabitants worship the first beast” suggesting it was in fact acting on behalf of the Roman Empire advocating that people worship the emperor. The reference to a mark on one’s hand and forehead is used in the Old Testament frequently as an idiom for devotion and appears to be used in this way in the very next verse in Revelation 14:1. What the text does then is warn against false prophets who, claiming to speak on behalf of God, command people to worship the state.
When one examines Revelation understanding its genre as apocalyptic genre, a literary style that is highly symbolic which uses stock symbols drawn from elsewhere in the Old Testament and pays attention to the symbols used then Revelation 13 does not teach the existence of a future anti-christ who implants the number 666 into people or advocates the kind satanic rituals described by Iron Maiden. What it teaches is that the state can be satanic; while Romans 13 teaches that the state is God’s servant, that it has legitimate authority to punish wrongdoing and commend those who do good, Revelation 13 warns that when the state makes itself into an empire, dominants the world by military power and demands absolute allegiance and devotion from human beings, it is satanic; it tempts human beings to be like God. Religious organisations that advocate this sort of statism may appear Christian but in fact are a dangerous temptation. Fidelity to God may mean refusing to give absolute obedience and allegiance to human rulers. This I think is an important message, one that should not be clouded or distorted by fantastic stores about future anti-christs, world governments, micro chips and barcodes.
 John AT Robinson Redating the New Testament (London: SCM Press, 1975) 236.
616, That Other Number of the Beast