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The University of Michigan, Ann Arbor (UM or U of M) is a coeducational public research university in the U.S. state of Michigan. Founded in 1817 some 20 years before the territory of Michigan officially became a state, the university moved to Ann Arbor in 1837. Today, it is the state’s oldest university and the flagship campus of the University of Michigan system.

Academically, the university is ranked among the world’s top universities. In 2007, U.S. News & World Report ranked the undergraduate division 24th in the U.S. UM has one of the largest research expenditures of any American university as well as one of the largest number of living alumni at 420,000. The university is also recognized for its history of student activism and its athletic teams, notably in football and ice hockey. However, despite being a public institution, the University of Michigan is also known for its high student fees; tuition for out-of-state students is currently the most expensive in the country.

UM was the first American university to use the seminar method of study. It was also the location chosen by President John F. Kennedy to propose the concept of what became the Peace Corps, and the site of Lyndon B. Johnson's speech outlining his Great Society program. More recently, the university was found in violation of the constitution for using race as a "primary" consideration in its undergraduate admission process. However, as far as graduate school is concerned, the University did successfully affirm before the U.S. Supreme Court that consideration of race as a "small and un-quantified" diversity factor in admissions to graduate programs within universities was constitutional.

The University of Michigan was established in 1817 by the Michigan Territory legislature on 1,920 acres (7.76 km²) in Detroit, land ceded through the Treaty of Fort Meigs by the Chippewa, Ottawa, and Potawatomi peoples. Ann Arbor had set aside 40 acres (16 ha) that it hoped would become the site for a new state capital, but it subsequently offered this land to the university when Lansing was chosen as the state capital. The university land in Detroit was sold, and the university moved to Ann Arbor in 1837. The original 40 acres in Ann Arbor became part of the current Central Campus.

The first classes in Ann Arbor were held in 1841, with six freshmen and a sophomore, taught by two professors. Eleven students graduated in the first commencement in 1845. By 1865 to 1866, the enrollment had increased to 1,205 students, many of whom were Civil War veterans. Women were first admitted in 1870, making the University of Michigan the third school to do so (after Oberlin College in 1833 and Lawrence University in 1847), some 100 years before most Ivy League schools. James B. Angell, who served as the university's president from 1871 to 1909, aggressively expanded UM's curriculum to include professional studies in dentistry, architecture, engineering, government, and medicine.

From 1900 to 1920 many new facilities were constructed on campus, including facilities for the dental and pharmacy programs, a chemistry building, a building for the natural sciences, Hill Auditorium, large hospital and library complexes, and two residential halls. The university's reputation for research gained momentum in 1920 with a formal reorganization of the College of Engineering and the formation of an advisory committee of 100 industrialists to guide academic research initiatives. During World War II, UM's research output grew significantly, and included major initiatives on behalf of the U.S. Navy, including advances in the development of proximity fuzes, PT boats, and radar jamming. By 1950, enrollment had reached 21,000, of whom 7,700 were veterans supported by the G.I. Bill. As the Cold War and the Space Race took hold, UM became a major recipient of government grants for strategic research and helped to develop peacetime uses for nuclear energy.

On March 24, 1964, a group of UM faculty members and 2,500 students held the nation's first ever faculty-led "teach-in" to protest against American policy in Southeast Asia. In response to a series of sit-ins in 1966 by Voice–the campus political party of Students for a Democratic Society–the U-M's administration banned sit-ins. This stimulated 1,500 students to conduct a further one-hour sit-in in the administration building.

During the 1970s, severe budget constraints hindered the university's physical development and academic standing. The 1980s saw a surge in funds devoted to research in the social and physical sciences. Meanwhile, the university's involvement in the anti-missile Strategic Defense Initiative and investments in South Africa caused controversy on campus. During the 1980s and 1990s, the university devoted substantial resources to renovating its massive hospital complex and improving the academic facilities on the North Campus. The university also emphasized the development of computer and information technology throughout the campus.

In 2003, two lawsuits involving UM's affirmative action admissions policy reached the U.S. Supreme Court (Grutter v. Bollinger and Gratz v. Bollinger). President George W. Bush took the unusual step of publicly opposing the policy before the court issued a ruling. The eventual ruling was mixed but the University of Michigan won the most important ruling at issue in those historical cases; that race may be considered as a factor in university admissions in all public universities and by private universities that accept federal dollars for such things as research or financial aid. In the first case, the court upheld the Law School admissions policy, while in the second it ruled against the university's undergraduate admissions policy. In the early 2000s, UM also faced declining state funding due to state budget shortfalls. At the same time, the university attempted to maintain its high academic standing while keeping tuition costs affordable. There were also disputes between UM's administration and labor unions, notably with the Lecturers' Employees Organization (LEO) and the Graduate Employees Organization (GEO), the union representing graduate student employees. These conflicts led to a series of one-day walkouts by the unions and their supporters.

The August 1, 2006, publication of The Advocate College Guide for LGBT Students highlighted the University of Michigan as one of the 20 best campuses for LGBT students. The guide acknowledged colleges and universities across the United States for making strides toward the advancement and integration of the LGBT community via a wide variety of student support groups, resources, events, policies, and other efforts to create an overall exceptional educational climate for these individuals.

The Ann Arbor campus is divided into three main areas: the North, Central and South Campi. The physical infrastructure includes more than 300 major buildings, with a combined area of more than 29 million square feet (2.69 km²). The campus also consists of buildings scattered throughout the city, many occupied by organizations affiliated with the University of Michigan Health System. The university also has an office building called Wolverine Tower in southern Ann Arbor near Briarwood Mall. Another major facility is the Matthaei Botanical Gardens, which is located on the eastern outskirts of Ann Arbor.

All three campus areas are connected by free bus services, the majority of which connect the North and Central Campi. There is a shuttle service connecting the University Hospital, which lies between North and Central Campi, with other medical facilities throughout northeastern Ann Arbor. The Central and South Campus areas are contiguous, while the North Campus area is separated from them, primarily by the Huron River.

The University of Michigan's sports teams are called the Wolverines. They participate in the NCAA's Division I-A and in the Big Ten Conference in all sports except men's ice hockey, which competes in the Central Collegiate Hockey Association. In seven of the past ten years, UM has finished in the top five of the NACDA Director's Cup, a ranking compiled by the National Association of Collegiate Directors of Athletics to tabulate the success of universities in competitive sports. UM has finished in the top eleven of the Directors' Cup standings in each of the award's twelve seasons and has placed in the top six in each of the last eight seasons. The University of Michigan remains the only school in NCAA history to win at least one national championship in all four of these sports: baseball, basketball (men's), football, and ice hockey (men's). The Wolverines have also won NCAA Division I national championships in women's field hockey, men's golf, men's gymnastics, women's softball, men's swimming and diving, men's tennis, and men's outdoor track and field.

The UM football team won the first Rose Bowl game in 1902, and through the 2005 season surpasses all other NCAA teams in both total wins (849) and winning percentage (.7442). The program is the only team to have been ranked in the final Top 20 (1985-88) or Top 25 (1989-2004) poll every year from 1985 to 2004. The last year in which UM did not receive a bowl game invitation was 1974, which was also the last season in which Big 10 teams other than the champion were not eligible for bowls; UM's last losing season was in 1967. Since 1989, the Wolverines have won outright or shared seven Big Ten titles and won a national championship. As mentioned above, UM football has won eleven national championships, the most recent in 1997, and has produced three Heisman Trophy winners: Tom Harmon, Desmond Howard and Charles Woodson.

Michigan Stadium is the largest college football-only stadium in the world, with an official capacity of more than 107,501 (the extra seat is permanently reserved for Fritz Crisler) though attendance—frequently over 111,000 spectators—often exceeds the official capacity. The NCAA's record-breaking attendance has become commonplace at Michigan Stadium, especially since the arrival of head coach Bo Schembechler (1969-1989). UM has fierce rivalries with many teams, including Michigan State and Notre Dame; however, its football rivalry with Ohio State is widely considered to be the fiercest in all of college athletics and has been referred to by ESPN as the greatest rivalry in American sports. Moreover, UM has an all time winning record in football against Notre Dame (19-14-1), Ohio State (57-39-6), and Michigan State (33-19-2).

The men's ice hockey team, which plays at Yost Ice Arena, has won an NCAA record nine national championships. The men's basketball team, which plays at Crisler Arena, won the national championship in 1989. However, the men's basketball program became involved in a scandal involving payments from a booster during the 1990s. This led to the program's being placed on probation for a four-year period, with a ban on postseason play from 2002 to 2003. The program also voluntarily vacated victories from past seasons.

The men's baseball team won national championships in 1953 and 1962 and has sent 138 players to the major leagues.

Michigan's men’s swimming and diving teams have won 11 NCAA and NCAA Division I national titles and 147 individual titles.

Through the 2004 Summer Olympic Games, 178 UM students and coaches had participated in the Olympics, winning medals in every Summer Olympics except 1896, and winning gold medals in all but four Olympiads. UM students have won a total of 116 Olympic medals including 54 gold, 27 silver, and 35 bronze.