The First Seal is opened, "1 Now I watched when the Lamb opened one of the seven seals, and I heard one of the four living creatures say with a voice like thunder, "Come!"2 And I looked, and behold, a white horse! And its rider had a bow, and a crown was given to him, and he came out conquering, and to conquer." (Revelation 6:1-2) The "Lamb" is Christ, as we learned in chapters 4-5. At the opening of the Seal the command, "Come" is given and a rider on a white horse comes forward with a bow. It is commonly thought that this is the antichrist who will conquer the world and reign over it. This also most likely lines up with the last week of Daniel's 70 weeks and with the "Prince who is to come." (Daniel 9:27)
The Beasts and the Mark of the Beast are introduced in chapter 13. There are dozens, if not hundreds of possible interpretations for this chapter, so I will just give the most basic interpretations. The first Beast that rises from the sea with 10 horns and 7 heads is commonly held to be the anticrist and the dragon who gives him authority is Satan. The second Beast rises from the land and has two horns like a lamb, but speaks like a dragon. This is generally thought to be the false prophet. This false prophet will perform miracles and lead worship of the first Beast. The mark of the Beast is given to us as 666, a human number, repeated three times, perhaps representing humanism/secular philosophy.
In chapter 7 we have the 144,000 sealed with a mark on their foreheads. This also can be interpreted many ways both literally and figuratively. From my reading this group is generally considered to be the remainder of the Church on earth. This seal is the antithesis of the mark of the Beast.
That's a quick overview and a very surface level look at this section of the Book of Revelation. I look forward to teaching this tonight.