13:1 Then I stood on the sand of the sea. I saw a beast coming up out of the sea,
 

having ten horns and seven heads
. On his horns were ten crowns, and on his heads, blasphemous names.
13:2 The beast which I saw was like a leopard,
and his feet were like those of a bear, and his mouth like the mouth of a lion.
The dragon gave him his power, his throne, and great authority.
13:3 One of his heads looked like it had been wounded fatally.
His fatal wound was healed, and the whole earth marveled at the beast.

13:4 They worshiped the dragon, because he gave his authority to the beast,
and they worshiped the beast, saying,
"Who is like the beast? Who is able to make war with him?"

13:5 A mouth speaking great things and blasphemy was given to him.
Authority to make war for forty-two months was given to him.
13:6 He opened his mouth for blasphemy against God,
to blaspheme his name, and his dwelling, those who dwell in heaven.

13:7 It was given to him to make war with the saints, and to overcome them.
Authority over every tribe, people, language, and nation was given to him.
13:8 All who dwell on the earth will worship him, everyone whose name has not been written from the foundation of the world in the book of life of the Lamb who has been killed.
 

13:9 If anyone has an ear, let him hear.
13:10 If anyone has captivity, he will go. If anyone is with the sword, he must be killed
.{TR reads "If anyone leads into captivity, into captivity he goes. If anyone will kill with the sword, he must be killed with a sword." instead of "If anyone has captivity, he goes away. If anyone is with the sword, he must be killed."}
Here is the endurance and the faith of the saints.

13:11 I saw another beast coming up out of the earth.
 

He had two horns like a lamb, and he spoke like a dragon.
13:12 He exercises all the authority of the first beast in his presence.
He makes the earth and those who dwell in it to worship the first beast,
whose fatal wound was healed.
13:13 He performs great signs,
even making fire come down out of the sky to the earth in the sight of people.
13:14 He deceives my own people who dwell on the earth because of the signs he was granted to do in front of the beast; saying to those who dwell on the earth,
that they should make an image to the beast who had the sword wound and lived.
13:15 It was given to him to give breath to it, to the image of the beast,
that the image of the beast should both speak,
and cause as many as wouldn't worship the image of the beast to be killed.

13:16 He causes all, the small and the great, the rich and the poor,
and the free and the slave, to be given marks on their right hands,
or on their foreheads;
13:17 and that no one would be able to buy or to sell,
unless he has that mark, the name of the beast or the number of his name.
13:18 Here is wisdom. He who has understanding,
let him calculate the number of the beast, for it is the number of a man.
His number is six hundred sixty-six.

"And the ten horns out of this kingdom are ten kings that shall arise: and another shall rise after them; and he shall be diverse from the first, and he shall subdue three kings. And he shall speak great words against the most High, and shall wear out the saints of the most High, and think to change times and laws: and they shall be given into his hand until a time and times and the dividing of time."Dan 7:24,25

What about the seven heads? "And here is the mind which hath wisdom. The seven heads are seven mountains, on which the woman sitteth." Rev 17:9 The Woman turns out to be a city. These hills could be the famous "seven hills of Rome" either literally or some modern day equivalent of what Rome was like in John's time.

vs 3 Some have speculated that the AntiChrist will be a Roman Emporer like Nero (whose name works out to be 666) will rise from the dead. Re 17:11 "And the beast that was, and is not, even he is the eighth, and is of the seven, and goeth into perdition."

"Whole" world is being used in a limitted categorical sense in that it doesn't include the redeemed. A similiar figure of speech can be found in John 12:19.

vs 5 The 42 months I infer to be the same 1260 days as mentioned throughout Revelations and Daniel (see the Timing Chart). This would mean that he would not have taken on this degree of authority or be worshipped in this manner until 3.5 years after he confirmed a covenant with many (Dan 9:27 He will confirm a covenant with many for one 'seven.' (7 years) In the middle of the 'seven' (3.5 years) he will put an end to sacrifice and offering.) The middle of the seven would begin the start of the 1260 days (42 months).

If I understand the timing correctly, during his first 3.5 years, the first few trumpets will also occur bringing much disaster. One could imagine the AntiChrist attributing the effects of the trumpets to his own innate powers and thus bring people to fear him.

vs 7 The war against the saints is during the 1260 day period in which many will be killed. Though believers won't be subject to God's wrath, they will be subject to persecution.

vs 8 It is inevitable that believers will not worship the beast, not because of their effort, but because their names have been written in the book of life. Thus their security is based on an absolute source. There are no people who are half-way believers. Either one has his name there, or he doesn't. In the end times, worshipping the beast could be considered a measure as to whether one has his name in the book of life. (It will be nice when things are so "black & white")

vs 10 Under such circumstances we must be prepared to behave as Christ did in approaching his crucifixion, as lambs to the slaughter. As such I wouldn't advocate a violent attempt to overthrow the AntiChrist, nor even violent resistance to persecution in such a circumstance. For he will be a legitimate authority figure, as Caesar was in his time. But rather to follow Christ's example. We must exercise patience and endurance of faith. For it has been characteristic of the saints to endure a great deal of persecution throughout history even from legitimate authority figures.

vs 11 The individual, called the "False Prophet" in Rev 16,19,20, was to given affirmation of the AntiChrist and promote the worship to the AntiChrist. I can only infer that the two horns represent two people who are as dragons in sheep's clothing. I suspect these are two ministers of the false prophet, in some way working for him.

vs 13 It is unclear whether these are miracles he is actually producing or simply deceiving people into believing he is producing. For example, as the seven trumpets are sounding during this time period, the first three trumpets all have something on fire falling from the sky. It could be that the false prophet takes credit for these, decieving the people.

vs 15 And one can easily image in this age of technology giving the impression of giving life to an idol.

vs 16-18 The famous mark of the beast. What is it really? Rev 14:11 indicates that all who receive the mark will be condemned. Yet obviously none of the redeemed do. "Forced" I think to mean "Coerced". Such coersion has no effect on the redeemed.

There are some Christians who are paranoid about accidently receiving this mark more than they are concerned about living proper Christian lives, as if God is so much concerned about such fleshly symbolic things. Rev 14:11,12 indicates that there will be a temptation presented to the "saints" to receive the mark. Most likely to recieve the mark, one must agree to worship the beast. This was somewhat the case with the early church during a certain time period. In order to escape persecution, one would make some nominal offering to Caesar. There were Christians who compromised in this area even in the early church, but the true believers - those whose names are written in the book of life - will not compromise, but endure to the end.

So what does "666" mean? "6" symbolizes "man". "3" symbolizes God as in the Trinity. So three 6's symbolize man making himself into God. However it has also been understood to represent an actual number which can be calculated from the person's name or title. In greek, numbers are represented by letters and thus by adding the letters up one comes up with a number for a person's name or title.

For example "Nero", one of the emporers had a number 666, as did one of the ways of writing "Roman Empire", but then again so does various spelling of "Bill Clinton", "Bill Gates", "Henry Kissenger", and a host of others. One can waste hours, even years of idle spectulation on this subject. Best to focus on things more edifying and substantive.