This is a very good book. It takes the subject seriously, but presumes no prior knowledge of kanji. The second half does assume you know kana, the two "alphabets" of 46 characters each. But to be honest, the whole book assumes you'll be studying diligently, and so requiring you to learn kana is minor compared to the task this book helps you with.
"Let's Learn Kanji" suits those with a structured mind. It builds up from strokes, to radicals and components, to 250 basic kanji which are themselves components of other kanji.
Most of the first half of the book consists of just tables of components, and it's tempting to skim them. Don't. Work through them carefully and several times, learning the names, shapes, and different example kanji which use each component. You'll need it when you come to the exercises, which are doable but challenging.
The second half of the book is a magnificent workbook of 250 kanji in stroke order. Each kanji is shown with all readings (pronunciations), example kanji which it forms part of, and example COMPOUNDS and SENTENCES with pronunciations and translations, as well as how to write it and space to practice writing it yourself. Again, these aren't to be skimmed, but worked through carefully. There are very useful exercises after every 20 or so to help fix them in your memory.
It's a pity it doesn't have a chart of hiragana and katakana, because after using romaji for Part 1 it switches to using kana for Part 2, and if you're not 100% sure of every kana then you'll want to print out your own chart to refer to. But this is a very minor flaw to an excellent book.
This is the best self-teaching beginner's book on kanji I've come across, and I strongly recommend it. You'll need dedication, but there are no lazy ways to learn kanji. If you're prepared to put effort in to studying, this is an excellent book to help you along the way.