The link is to the edition I read, there are a bunch out there. My complaint with this edition was that the maps were WAY too compressed to be useful.
Grant is such a towering figure in history that multiple biographies need to be read to get a glimpse of the man. I would say that starting your journey here is a better way to place Grant in US history.
What this book provides is an interior view of a brilliant general and what goes into the craft of war.
Logistics, logistics, logistics is a good start. The intricate dance between moving armies of tens of thousands of men (and horses in those days), plus food, ammo, medical services, communications (telegraph back then), and countless other factors loom large.
Understanding the personalities of your subordinates and your adversaries is also key. Some generals are overly cautious, others are overly aggressive. Some need to be given strict and very detailed orders, since they really don't want to take responsibility for anything but success. If the battle is won, they love to report their brilliant moves ... if it fails, they will produce your detailed orders to show that "they were only following orders".
The influence of media was strong factor even then. The media tended to idolize the brilliance of the dashing Lee, while poking fun at the apparently hapless Northern generals. Grant says nearly nothing about the problems of the Army of the Potomac. He does point out the criticality of the victory at Gettysburg, and Vicksburg happening on the same 4th of July as likely saving the Union. Yet another book I'd like to read ... "The Most Glorious 4th".
In the press, Lee was portrayed as a brilliant tactician, with nothing of his strategic advantages being pointed out. Grant was portrayed as a "butcher" ... a man of little intelligence and poor character. The mostly apocryphal stories of him as a "drunk", are crafted by his competitors and detractors from his time alone in California, when he did drink to excess, or from injuries sustained that were attributed to him being drunk by his enemies, but not supported by evidence. Neither alcohol or cigars are discussed in the book ... the cigars likely because he was dying of painful throat cancer as he struggled to write the book.
When he was writing this, he was virtually penniless, and the sales of the book were his only option to provide something for his family after he passed. He finished the manuscript on July 18, 1885. He died five days later on July 23. Mark Twain was a huge factor in his writing of the book and it's promotion (also not mentioned in the book).
The South was fighting on their home turf, defending their entire way of life. They were on defense. Clausewitz said that as a general rule of thumb, attacking forces have to be at least three times stronger than defending forces.Given these facts ... largely ignored in reporting at the time, and even in history, the North was at grave disadvantage because their strength rarely if ever approached those ratios, In fact, the South often brought greater force. When Lee went on offense at Gettysburg, he lost.
"The fact is the Constitution did not apply to such contingency as the one existing from.1861 to 1865. Its framers never dreamed of such a contingency occurring. If they had forseen it, the probabilities are they would have sanctioned the right of a State or States withdraw rather than that there should be war between brothers."
There are many ironies of the Civil War, but one of the big ones is that the Democrats were the "conservatives", concerned with the Constitution, and tradition. The Republicans were the "radicals", willing to risk life and treasure for an idea, and their view of "righteousness".
Whole books are written on the issue of whether the Civil War effectively killed the Constitution and initiated the idea of "progressivism" in the US ... a subject to long and complicated to go into here.