Ad&d second edition is in some ways a forgotten edition of Ad&d. people remember basic for being the first, they remember 1st edition due to the great modules and expansion of the game. 3rd recreated the system and tried and failed to simplify it. 4e is a love it or hate it system that almost destroyed the game line, and 5e is a throwback to older times and was made to appeal to everyone. 2e on the other hand is the edition stuck between the juggernauts of 1e and 3e. the rules are a cleaned up more or less streamlined update of first edition. the rules are close enough that you can convert whole modules and supplements with almost no change.
second edition for good or ill brought bloat into the game with hundreds of supplements and rule expansions. first edition focused on modules, and had only a few major rules supplements. the other thing that second brought to the table was the expanding of campaign settings, such as dragonlance, dark sun, Ravenloft, birthright and planescape. now some of those did begin in first edition, but second edition cranked up the release schedule of those settings. this sadly thinned the fan base a lot and hurt the game in the long run as well as being a factor in Wizards of the coast buying out TSR.
some great things did come out of 2e though. the first was THAC0. now love it or hate it THAC0 was an improvement over having to look up your to hits on a chart all the time. the second and my favorite was specialty priests. no longer would every cleric have the same spell selection, instead a priest of the god of war could have completely different spells from the god of peace and love. too bad the whole flawed concept of balance has led to the end of that idea and now all clerics again are basically the same spell wise. it was good while it lasted.
Obviously if you want to get into second edition you will need this book and I personally love second edition it may be my favorite D&D edition, though 5e is giving it a run for its money as they say.