TLDR: I just started working out for pretty much the first time in my life about a month ago and got recommended this book somewhere. I found it pretty understandable at a beginner level and feel like I learned a lot. Def would recommend it.
Before I get into the specifics of what his program is, I have to say I enjoyed Pavel's constant invocations of Communist and Soviet history. I'm sure it was largely to differentiate himself from the other exercise books on the market and play into the stereotype of Russian bear strength but I still enjoyed being called "Comrade" and learning the "Communist Way" to work out.
Essentially, Pavel is arguing that standard American weightlifting is overcomplicated and more in service of the appearance of strength rather than actual strength. He rails against exercise machines as they don't allow you to use your "stabilizing muscles" and more or less only train you to lift heavier things on the machine rather than actual heavy things in real life. He also finds fault with the "work out 'til you drop" mentality some people have, using scientific evidence to argue that in fact working less hard will lead to greater results. Apparently, muscle building happens during the recovery process and not during the lifting, who knew.
Anyway, what HE believes is the ideal strength training program is a simple mix of deadlifts, presses (side presses specifically), and maybe a curl at the end (not necessary though.) Deadlifts and presses should both be done with two sets of five reps with heavy weight, with a minute and a half rest between each set and taking at least 5 seconds on each rep to maximize tension. The second set should be slightly lighter than the first set for both of the above, and more sets can be added with a gradually reducing weight.
Three main concepts addressed are "cycling," "power breathing," and "tension." Cycling prevents the body from becoming too used to the workout and reaching a dead end. Essentially, over let's say a 10 day period more and more weight is added at each day. At the end of the cycle, you switch back to a much lighter weight than the one you capped at and begin the cycle over again. Constantly lifting the maximum amount you can is actually counter-productive to muscle gain. Power breathing is all about filling your lungs with air and holding it until the middle part of the lift, then releasing half of your breath to give you additional power. "Hold your breath (keep your glottis closed) as you are lowering and lifting the weight. Exhale near the end of a rep, or right after it." Apparently this is a karate trick. The third concept is about maximizing tension means maximizing strength. He uses professional arm wrestlers as an example, as well as the old concept of "dynamic tension" in which just tensing up your muscles and lifting literally nothing can lead to strength gain. You should tense up your muscles before you even touch the weight.