Google Page Rank, Analysis and Search engine optimisation

Google Page Rank
PageRank is a link analysis algorithm, named after Larry Page, used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. The university received 1.8 million shares of Google in exchange for use of the patent; the shares were sold in 2005 for $336 million.
SEO
Search engine optimization (SEO) is the practice of maximizing the volume or quality of traffic to a web site (such as a blog) from search engines via "natural" or un-paid ("organic" or "algorithmic") search results as opposed to other forms of search engine marketing ("SEM") which may deal with paid inclusion. The theory is that the earlier (or higher) a site appears in the search results list, the more visitors it will receive from the search engine. SEO may target different kinds of search, including image search, local search, video search and industry-specific vertical search engines. This gives a web site web presence.
As an Internet marketing strategy, SEO considers how search engines work and what people search for. Optimizing a website primarily involves editing its content and HTML and associated coding to both increase its relevance to specific keywords and to remove barriers to the indexing activities of search engines.
PPC
Pay Per Click (PPC) is an Internet advertising model used on websites, in which advertisers pay their host only when their ad is clicked. With search engines, advertisers typically bid on keyword phrases relevant to their target market. Content sites commonly charge a fixed price per click rather than use a bidding system.
Cost per click (CPC) is the amount of money an advertiser pays search engines and other Internet publishers for a single click on its advertisement that brings one visitor to its website.
In contrast to the generalized portal, which seeks to drive a high volume of traffic to one site, PPC implements the so-called affiliate model, that provides purchase opportunities wherever people may be surfing. It does this by offering financial incentives (in the form of a percentage of revenue) to affiliated partner sites. The affiliates provide purchase-point click-through to the merchant. It is a pay-for-performance model: If an affiliate does not generate sales, it represents no cost to the merchant. Variations include banner exchange, pay-per-click, and revenue sharing programs.
Websites that utilize PPC ads will display an advertisement when a keyword query matches an advertiser's keyword list, or when a content site displays relevant content. Such advertisements are called sponsored links or sponsored ads, and appear adjacent to or above organic results on search engine results pages, or anywhere a web developer chooses on a content site.
Although many PPC providers exist, Google AdWords, Yahoo! Search Marketing, and Microsoft adCenter are the three largest network operators, and all three operate under a bid-based model. Cost per click (CPC) varies depending on the search engine and the level of competition for a particular keyword.
The PPC advertising model is open to abuse through click fraud, although Google and others have implemented automated systems to guard against abusive clicks by competitors or corrupt web developers.