fredthebear: Do read Renaud and Kahn's classic book "The Art of the Checkmate"! It has been reprinted in algebraic notation (abbreviated AN or FAN) for those who skip the joy of descriptive notation (abbreviated DN) books.
Keep in mind that many of the mating patterns in "The Art of the Checkmate" feature some of the all-time great finishes, so don't expect the book to be an easy cake walk. However, there are enough diagrams at the critical moment of the game to assist the determined reader.
"The Art of the Checkmate" is for knowledgeable intermediate level players who have prior experience solving tactics and combinations as well as replaying written tournament games of master players. It is often mislabeled as a beginners book.
Descriptive notation (DN) readers probably should read "How to Force Checkmate" by Fred Reinfeld first. It contains 300 diagrams of progressive checkmate puzzles in 1, 2, and 3 moves. Every puzzle ends in checkmate; it does not explain other aspects of chess as most of Reinfeld's books do. A beginner certainly cannot play like Dr. Tarrasch did in the game above, and is not ready to analyze in such a manner!
Algebraic notation (AN or FAN) readers should tackle "Checkmate for Children" by Kevin Stark and/or "How to Beat Your Dad at Chess" by Murray Chandler first. Don't let the titles fool you -- grown-ups will benefit from these training books because of the variety of patterns included. A.J. Gillam has a simpler, less colorful series of out-of-print tactics training books that are recommended if purchased at a discount. There are plenty of other good modern choices written in algebraic notation, but descriptive notation tends to be written for stronger club players and masters (unless Fred Reinfeld wrote it by himself).
ALL beginners eleven years or older (or any adult player who knows the moves and rules but is struggling to improve) should read the best seller "Bobby Fischer Teaches Chess". It asks only one question per page and uses stars and arrows instead of notation for simplicity. Read BFTC again and again until the student can answer each puzzle correctly. There's no point to study much of anything else until BFTC becomes easy for the student to solve. After reading BFTC 3 or 4 times, perhaps 5 or 6 times if necessary, from cover to cover, the reader will be instilled with confidence as they learn to accurately solve the checkmate puzzles. In fact, re-reading any chess book is generally good advice. Unfortunately, other chess books about Bobby Fischer are too advanced for beginners.
It's better to read a chess book that is too easy but enjoyable than a book that is too difficult to comprehend. Furthermore, don't let the cover title fool you! "Basic" or "Fast" on the cover does not always mean basic/fast reading inside. In general, the new chess student needs plenty of stimulating pictures/diagrams and shorter sentences/paragraphs.