Alger was born in Lafayette Township, Medina County, Ohio. He was orphaned at twelve and worked on a farm; attended Richfield Academy in Ohio and taught school for two winters. Later, he studied law, was admitted to the bar, and began practice in Cleveland, 1859.
Mr. Alger moved to Grand Rapids, Michigan in 1860; and married Annette Henry in 1861.
Mr. Alger was governor of Michigan, 1885–1886. He was elected by his comrades as commander of the Grand Army of the Republic in 1889 and served as Secretary of War, 5 March 1897–1 August 1899.
He was criticized for the inadequate preparation and inefficient operation of the department during the Spanish-American War, and resigned at President McKinley’s request. In 1899; he published The Spanish-American War in 1901. He was appointed to serve out the unexpired term of the deceased James McMillan in the U.S. Senate in September 1902. He was elected in his own right and served in the Senate, 1903–1907.
Mr. Alger died in Washington, D.C., on 24 January 1907.