2003–2006: Thefacebook, Thiel investment, and name change
Zuckerberg wrote a program called "Facemash" in 2003 while attending Harvard University as a sophomore (second year student). According to The Harvard Crimson, the site was comparable to Hot or Not and used "photos compiled from the online facebooks of nine Houses, placing two next to each other at a time and asking users to choose the "hotter" person". Facemash attracted 450 visitors and 22,000 photo-views in its first four hours online. The Facemash site was quickly forwarded to several campus group list-servers, but was shut down a few days later by the Harvard administration. Zuckerberg faced expulsion and was charged by the administration with breach of security, violating copyrights, and violating individual privacy. Ultimately, the charges were dropped.Zuckerberg expanded on this initial project that semester by creating a social study tool ahead of an art history final exam. He uploaded all art images to a website, each of which was featured with a corresponding comments section, then shared the site with his classmates, and people started sharing notes.A "face book" is a student directory featuring photos and basic information.In 2003, there were no universal online facebooks at Harvard, with only paper sheets distributed and private online directories. Zuckerberg told the Crimson that "Everyone’s been talking a lot about a universal face book within Harvard.  I think it’s kind of silly that it would take the University a couple of years to get around to it. I can do it better than they can, and I can do it in a week."In January 2004, Zuckerberg began writing code for a new website, known as "TheFacebook", with the inspiration coming from an editorial in the Crimson about Facemash, stating that "It is clear that the technology needed to create a centralized Website is readily available ... the benefits are many." On February 4, 2004, Zuckerberg launched "TheFacebook", originally located at thefacebook.com.

Six days after the site launched, Harvard seniors Cameron Winklevoss, Tyler Winklevoss, and Divya Narendra accused Zuckerberg of intentionally misleading them into believing that he would help them build a social network called HarvardConnection.com. They claimed that he was instead using their ideas to build a competing product. The three complained to The Harvard Crimson and the newspaper began an investigation. They later filed a lawsuit against Zuckerberg, subsequently settling in 2008 for 1.2 million shares (worth $300 million at Facebook's IPO).

Membership was initially restricted to students of Harvard College; within the first month, more than half the undergraduates at Harvard were registered on the service. Eduardo Saverin, Dustin Moskovitz, Andrew McCollum, and Chris Hughes joined Zuckerberg to help manage the growth of the website. In March 2004, Facebook expanded to the universities of Columbia, Stanford, and Yale.It later opened to all Ivy League colleges, Boston University, New York University, MIT, Washington and gradually most universities in the United States and Canada.

In mid-2004, entrepreneur Sean Parker—an informal advisor to Zuckerberg—became the company's president. In June 2004, Facebook moved its operations base to Palo Alto, California.It received its first investment later that month from PayPal co-founder Peter Thiel.In 2005, the company dropped "the" from its name after purchasing the domain name facebook.com for US$200,000.The domain facebook.com belonged to AboutFace Corporation before the purchase. This website last appeared on April 8, 2005;[25] from April 10, 2005, to August 4, 2005, this domain gave a 403 error.