Theodore Roosevelt campaigned for election to the office of the presidency two times. He was elected as vice-president when William McKinley was elected as president in the 1900 election. At that time, terms for president and vice-president began in March, not Jan. 20 as is now the practice. Pres. McKinley was assassinated and Pres. Roosevelt was sworn into office on Sept. 14, 1901, so he didn't actually run for the presidency prior to his first term in office. He did run for reelection in 1904 and won easily.
Roosevelt endorsed Taft for the presidency in the 1908 election but was dismayed with the direction in which Pres. Taft took the government. Roosevelt was unable to regain the Republican nomination for the presidency as the 1912 campaign approached, so he and his followers formed a third political party, popularly known as the Bull Moose Party, and Roosevelt campaigned for election under that party's sponsorship. He lost the election to Woodrow Wilson, but did gain more of the popular vote than did Pres. Taft.