The dragon has seven heads, with seven crowns on those heads:

Revelation 12:3 And there appeared another wonder in heaven; and behold a great red dragon, having seven heads and ten horns, and seven crowns upon his heads.

Then, the chip off the ole block, the beast, also has seven heads, with the name of blasphemy upon the heads:

Revelation 13:1 And I stood upon the sand of the sea, and saw a beast rise up out of the sea, having seven heads and ten horns, and upon his horns ten crowns, and upon his heads the name of blasphemy.

But, then, one of those seven heads was, as it were, wounded to death:

Revelation 13:3 And I saw one of his heads as it were wounded to death; and his deadly wound was healed: and all the world wondered after the beast.

Then the woman is sitting on beast with seven heads:

Revelation 17:3 So he carried me away in the spirit into the wilderness: and I saw a woman sit upon a scarlet coloured beast, full of names of blasphemy, having seven heads and ten horns.

Then there is not only the mystery of the woman, but apparently the mystery of the beast with seven heads:

Revelation 17:7 And the angel said unto me, Wherefore didst thou marvel? I will tell thee the mystery of the woman, and of the beast that carrieth her, which hath the seven heads and ten horns.

And then it says:

Revelation 17:9 And here is the mind which hath wisdom. The seven heads are seven mountains, on which the woman sitteth.

  10 And there are seven kings: five are fallen, and one is, and the other is not yet come; and when he cometh, he must continue a short space.

From which many conclude that the seven heads are the seven hills of Rome (I used to believe that, too, for many years, after I got saved).

However, if the seven heads are the seven hills of Rome, that leaves some difficulties understanding the other lines.

Like in 12:3, there are seven crowns on the seven heads, so, are there seven crowns on the seven hills of Rome?

Or in 13:1, the name of blasphemy is on the seven heads, so, is there the name of blasphemy upon the seven hills of Rome?

But in 13:3, one of the seven heads was, as it were, wounded to death, so is one of the seven hills of Rome to be wounded to death?

Then in 17:3, what relation would there be between the wilderness and the seven hills of Rome?

So, in 17:7, if the mystery of the woman is that she is the catholic vatican of Rome, and the mystery of the beast with seven heads are the seven hills of Rome,

then who, or what, would the ten horns of Rome supposed to be?

In 17:9 the seven heads are said to be seven mountains, not seven hills, but then it immediately, in 17:10, ties the seven mountains with seven kings.

So, then, who are the seven kings of Rome supposed to be?

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