If you are serious about improving your Web site relevance on Google (and as a consequence on several other major search engines) you should understand quite well what Pagerank is and how it works.

Pagerank is a an algorithm that Google utilizes to rank its search results in presence of multiple resources matching a certain query. In very simple words Pagerank evaluates and ranks Web sites according to a computed value determined by the number of other sites linking to them. The way the Pagerank value is computed makes Pagerank somewhat immune to artificial linking efforts.

In order to provide the greatest understanding and to allow an exhaustive mini-guide to Pagerank understanding I have researched and listed here below the most interesting and valuable resource on this topic that are available online.
Including the original Stanford paper from which the whole thing started.

1) The original PageRank paper by Google's founders
Sergey Brin and Lawrence Page:
The Anatomy of a Large-Scale Hypertextual Web Search Engine
http://www-db.stanford.edu/~backrub/ google.html

2) What can you do with a Web in your Pocket
by Sergey Brin, Rajeev Motwani, Larry Page und Terry Winograd
Web Archive

3) The PageRank Citation Ranking: Bringing Order to the Web
by Lawrence Page, Sergey Brin, Rajeev Motwani und Terry Winograd
http://dbpubs.stanford.edu:8090/pub/ showDoc.Fulltext?lang=en&doc= 1999-66&format=pdf&compression=

4) Efficient Crawling Through URL Ordering
by Junghoo Cho, Hector Garcia-Molina and Lawrence Page
http://dbpubs.stanford.edu:8090/pub/ showDoc.Fulltext?lang=en&doc= 1998-51&format=pdf&compression=

5) Attack Resistant Trust Metrics
Draft of PhD thesis in compact formatting by Raph Levien
http://www.levien.com/thesis/compact.pdf

6) United States Patent 6,285,999:
Method for node ranking in a linked database
http://164.195.100.11/netacgi/ nph-Parser?Sect1=PTO1&Sect2= HITOFF&d=PALL&p=1&u=/netahtml/ srchnum.htm&r=1&f=G&l=50&s1 ='6,285,999'.WKU.&OS=PN/ 6,285,999&RS=PN/6,285,999

7) Google PageRank web site http://pr.efactory.de/ This Web site is devoted exclusively to Google Pagerank. Its sections are devoted to: Pagerank algorithm, Implementation, Inbound and Outbound Links, Number of Pages, Yahoo bonus, Additional Factors and more. It provides also a valuable guide on how to compute your Pagerank without using the Google toolbar.
http://pr.efactory.de/ e-pagerank-implementation.shtml

8) Pagerank explained correctly and with examples
http://www.iprcom.com/papers/pagerank/

9) Pagerank. Google's PageRank and how to make the most of it
http://www.webworkshop.net/ pagerank.html
with Phil Craven's PageRank Calculator
http://webworkshop.net/ pagerank_calculator.html

10) PageRank Explained PLUS Copywriting Case Study
http://www.rankwrite.com/archives/ issue070.htm

11) PageRank Explained
http://www.webrankinfo.com/english/ pagerank/index.php

12) Chris Ridings' "PageRank Explained" paper
http://www.goodlookingcooking.co.uk/ PageRank.pdf

13) Mark Horrell's Web Site - PageRank Calculator
http://www.markhorrell.com/tools/ pagerank.html

14) Google Pagerank
http://www.googlerank.com/ranking/ pagerank.html

15) Pagerank for Sale
http://www.pandia.com/features/ pagerank.html
http://www.pandia.com/features/ pagerank2.html
http://www.pandia.com/features/ pagerank3.html

16) The Handy Dandy Google Page Rank Figurin' Guide
by Chris Raimondi
http://www.searchnerd.com/pagerank/

17) Online Discussion Forums on PageRank:

MarketPositionTalk - PageRank updates
http://www.marketpositiontalk.com/ forums/index.cfm?cfapp=11

SearchEngineForums - PR documents and calculator
http://www.supportforums.org/pagerank/

WebmasterWorld - PR document and calculator
http://www.webmasterworld.com/

Search Engine Forums - Google Forum
http://searchengineforums.com/bin/ forumdisplay.cgi?action=topics&forum= Google&number=28&DaysPrune=20& LastLogin=