The title tag is critical
The title tag is the single most important piece of content for people who search.
Keep it short: Don’t have more than 60 characters (with spaces), which is roughly 8-10 words.
Lead with the most important careword for that particular page. Always start off with what is specific about the page and move to what is general. Many websites begin their title with their brand or organization name, and then follow with what is unique about the page. (This is a very common mistake, so check out your website.)
The description tag is recommended
The description tag is not nearly as important as the title. However, it does have some value. Write it as a summary and keep it under thirty words. It should be written in a compelling, clear manner.

Light pages, and lean, quality HTML
The less HTML code you have, the better, as it makes it easier and faster for the search engine to index your page. Aim for a total page weight of 50 KB for any page (that’s including graphics). Certainly, anything over 100 KB is going to be slow, and some search engines don’t like pages that are over 100 KB.

Have a site map/index
People like site maps/indexes, and so do search engines. Make sure that the site map is available from the homepage, that it is presented in a text-based format, and that it is kept up to date.

Avoid Flash
I’ve nothing against Flash design except for the fact that I generally detest it. It’s such a waste of time; fourth rate TV advertising by people who will never get the chance to do a real TV ad. Search engines don’t like Flash either, and find it very hard to index Flash-based pages.

Build your website in static HTML
You don’t need a “dynamic” website unless you have dynamic content, such as airline seat availability and pricing which needs to be dynamically published from a database because it constantly changes. You may store your website in a database but you’re better off publishing it as a static HTML website. It’s cheaper, the pages will download faster, and search engines will find it easier to comprehensively index your website.

Avoid PDFs
One of the sure signs of a badly managed website is that it has lots of PDFs. Publishing content in PDF is usually a shortcut. Search engines have got better at indexing PDFs but it is still recommended that you publish a heading and summary in HTML.

Avoid frames
Frames are a very bad idea.

Watch your JavaScript
Any links that you have in JavaScript should also be published in HTML, otherwise the search engine won’t be able to follow those links. Rollovers are cool but they cause nothing but problems, so unless you have a brilliant technical team, avoid them.

Alternative text
As a rule you should have alternative text for every single image. However, the only alternative text that search engines recognize is for those images that are linked. Make sure you use descriptive, careword-rich text.

Keyword tags
Over the years, some websites tried to trick search engines by stuffing keyword tags with lots of popular words. Because of this, most search engines give very little value to keyword tags

A Survey of Google’s PageRank
Calculation of Page Rank, Page Rank Implementation, Inbound Links, Outbound Links, Number of Pages, PageRank Distribution, Additional Factors and more.
The Lineal Algebra Behind Google
The $25,000,000,000 Eigenvector - The Linear Algebra Behind Google. Google’s success derives in large part from its PageRank algorithm, which ranks the importance of webpages according to an eigenvector of a weighted link matrix. Analysis of the PageRank formula provides a wonderful applied topic for a linear algebra course.
The Intelligent Surfer: Probabilistic Combination of Link and Content Information in PageRank

We propose to improve Page-Rank by using a more intelligent surfer, one that is guided by a probabilistic model of the relevance of a page to a query. Efficient execution of our algorithm at query time is made possible by precomputing at crawl time (and thus once for all queries) the necessary terms.

Topic-Sensitive PageRank
To yield more accurate search results, we propose computing a set of PageRank vectors, biased using a set of representative topics, to capture more accurately the notion of importance with respect to a particular topic. By using these (precomputed) biased PageRank vectors to generate query-specific importance scores for pages at query time, we show that we can generate more accurate rankings than with a single, generic PageRank vector.

Method for node ranking in a linked database
A method assigns importance ranks to nodes in a linked database, such as any database of documents containing citations, the world wide web or any other hypermedia database. The rank assigned to a document is calculated from the ranks of documents citing it. In addition, the rank of a document is calculated from a constant representing the probability that a browser through the database will randomly jump to the document. By Page and Lawrence.

How Google Finds Your Needle in the Web’s Haystack
Mathematical Background of Google PageRank. By David Austin, Grand Valley State University
A Large-Scale Hypertextual Web Search Engine
Original Slides, by Larry Page.
Wikipedia: PageRank
Mathematical Theory Behind Google PageRank