I've yet to come across any reputable SEO books, but there are approaches to SEO worth learning.
First off, the algorithms that Google/Yahoo/Bing! use are irrelevant. Modern search engines have advanced to the point that they behave mostly as they should (despite the best efforts of the SEO industry). Beyond the fundamental principles of PageRank, no one really knows how Google's algorithms work. There are press releases about new search features and fixes to previous search problems, but the details of each ranking system's implementation is mostly speculative. Pretty much all of the information published by 3rd parties is based on finding vague statistical correlations and speculating on these "ranking factors".
So if you take the blackhat approach to SEO, i.e. trying to game the ranking algorithms, you won't find much concrete information to go on. And the frequent algorithm changes/fixed that are designed to combat blackhat techniques mean that any effective technique will just backfire in the long run.
But if you take the whitehat approach to SEO recommended by Google and other search engines, then you don't need to worry about the lack of detailed ranking algorithm information or the constant algorithm changes. That's because whitehat SEO really is just trying to make a useful and accessible website. This is much harder to do if you're a fly-by-night operation attempting to make a quick buck without providing anything of value to users. But if you started a site based on the genuine desire to provide useful information or services, then SEO will just be a natural side-effect of improving your website for users.
This also explains the lack of reputable books on SEO. Most SEO practices really fall into usability and accessibility best practices (e.g. using clean URLs, proper semantic markup, RESTful architecture, etc.), while others are just commonsense (like using good grammar/spelling, providing unique/useful/relevant content, etc.). So get a book on usability and optimizing web navigation, as well as study up on semantic HTML standards (like the proper use of
link tags) and Web Content Accessibility Guidelines. This type of SEO requires you to be invested in the long-haul, but it guarantees good results no matter how search engines adapt and evolve over time.
Lastly, you should be warned that the majority of the SEO industry that claims to be "whitehat" is actually in the greyhat category. SEO, as a marketing-based industry, is rather devoid of morals. Really, the majority of SEO professionals seem to eschew well known blackhat techniques like link farming and keyword stuffing simply because the search engines have wised up to them (most of the old-timers themselves practiced these techniques before they were penalized by search engines and labeled blackhat).
So be careful about whom you listen to. Even if something doesn't hurt your search ranking, it could still permanently damage your online reputation. This is especially pertinent considering that most "whitehat" SEOs (including the top SEO sites) still consider content-spinners and blog spamming acceptable forms of SEO. They might add a little disclaimer like "be sure your comment is useful and don't post to the same blog too many times in a row", but they still encourage webmasters to actively seek out unprotected blogs that don't inject
nofollows into links (e.g. on "high value" .edu sites) and post comments linking to yourself to game the PageRank system. And in that respect, SEO isn't really worth investing in explicitly for legitimate businesses and site owners. These types of practices that are pursued solely for the purpose of improving one's search ranking without improving user experience actually de-optimize search engine results and put you on the same level as spammers.