You bought the book without checking it out first ? If you have any tournament chess playing friends they can probably help you out....
Modern Chess Openings

It's not as complicated as it looks, you'll get used to it pretty quickly. It's actually quite simple. I personally like it better than NCO/ECO type tables.
I hope this picture will help you understand and not confuse you even more :)
The table covers the Latvian Gambit, starting from the moves 1. e4 e5 2.Nf3 f5.
6 different variations are covered in the table, one variation in each of the columns.
The numbers on the left represent the move numbers.
So the first variation in column 1 goes: 1.e4 e5 2.Nf3 f5 3.Bc4 fxe4 4.Nxe5 Qg5 5.d4 Qxg2 6.Qh5+ and so on.
The second variation starts on move 4 for Black, as you can tell from the dots before d5, meaning the moves before it were the same. So the second variation covered is 1.e4 e5 2.Nf3 f5 3.Bc4 fxe4 4.Nxe5 d5. 5.Qh5+ etc.
In the 6th variation you can see that it only starts on the 6th move because the moves before it were the same as in the 5th variation.
Also there are the footnotes which cover less common alternatives and if they're are the end of variations (as is the case in every column on this page) then the note will usually give a possible continuation with an evaluation of the position.
The book also uses evaluation symbols, like +- and so forth, those are covered in beginning of the book.

Jontsef, I know your post was from nine years ago, but it has just helped me tremendously. Thank you!

Any hope of having the image replaced?
This is the imagine of MCO Latvian Gambit.
Thanks

You should have looked at the pdf excerpt before buying the book. It should be in Arab notation. Quality Chess for example has all their books like that in this photo I took from one of their pdf excerpts. Notice how nice it is to read. You should in this case use a real board or if you want to save all the moves in a pgn for later with the comments and sidelines, use Lichess studies or Chess.com analysis/library

tryng to understand it But what are those dotted lines mean
The MCO is read in the other direction to the ECO, so the move list is on the left, and the variation number is on the top. The dots in variation two for move three mean that it's the same as variation one. In this case, I think the second variation reads like this:
1.e4 e5 2.Nf3 f5 3.Bc4 fxe4 4.Nxe5 d5 etc

Also, you can probably interpret much of the text in the footnotes in terms of evaluation notation. So, for instance, when it reads, 5.Bf7+ Ke7 6.Bb3 d5 is probably a little better for White, my guess is that you could write that out as:
5.Bf7+ Ke7 6.Bb3 d5 ⩲
and that they're deliberately rendering in the English language what was originally one of those symbols. Though, again, that's really a guess. I found this post just now doing a Google search, because I'm trying to figure out how to read the MCO. It just so happened that you were trying to discover the same thing on the same day.

I'm working over on p. 155, Unusual Double King Pawn Openings. The first two variations are the Hungarian Defence. This is what I wrote out for variation one:
1.e4 e5 2.Nf3 Nc6 3.Bc4 Be7 4.d4 d6 ( 4...exd4 5.Nxd4 d6 6.Nc3 Nf6 7.O-O O-O 8.h3 Nxd4 9.Qxd4 c6 10.a4 $14 { Spassky - Hort, Reykjavik 1977 } ) 5.d5 ( 5.dxe5 dxe5 ( 5...Nxe5 6.Nxe5 dxe5 7.Qh5 $16 ) 6.Qxd8+ ( 6.Bd5 Bd7 7.Ng5 Bxg5 8.Qh5 $14 { Bronstein - Scherbakov, USSR 1955 } ) 6...Bxd8 7.Nc3 Nf6 $14 { Van der Wiel - P. Nikolic, Malta 1980 } ) 5...Nb8 6.Bd3 ( 6.Nc3 Nf6 7.h3 c6 $10 { Chekover - Rabinovich, USSR 1938 } ) 6...Nf6 7.c4 O-O ( 7...Nbd7 8.Nc3 Nf8 9.h3 Ng6 10.O-O O-O 11.Be3 Nh5 12.Re1 Nhf4 13.Bf1 f5 14.Kh2 Qe8 15.exf5 Bxf5 16.Ng1 $14 { Lukovnikov - Malevinsky, USSR 1976 } ) 8.h3 ( 8.Nc3 c6 9.O-O Nbd7 10.Rb1 Re8 $10 { Mestel - Smyslov, Las Palmas 1982 } ) 8...Nbd7 9.Nc3 Ne8 ( 9...Ne8 10.O-O g6 11.Bh6 Ng7 12.Qe2 $14 { Fuchs - Kholmov, USSR 1967 } ) *
If you save that as a PGN file you can work with it. On this site it looks like this:

I was confused about this as well. But this thread helped me. For the dotted lines, Yeah looking back at the Latvian table. White has four serious replies to f5. Varaition #1 and #2 both play Bc4. If there isn’t any dots the variation just continues down the row. Reading chess tables has different rules like reading manga but once you learn them it makes more sense.
Help! I just purchased a copy of Modern Chess Openings 14th Edition, and I'm not sure how to read it properly. It's probably easier than I think, but I'm a little confused...maybe more than a little. Thanks!