The Right Stuff
The first program to put a man in space was the Soviet Union's Vostok program, so the second manned space program would be the US Mercury program. The second US manned program was Gemini.
The Mercury Program was the first manned space flight program,
The Gemini Program
The Geminii program
The objectives of the program, which made six manned flights from 1961 to 1963, were specific: To orbit a manned spacecraft around Earth;
Gemini.
Gemini
Gemini
Mercury.
The manned lunar landings were part of the US's Apollo program.
Mercury
The Apollo 11 mission was the first manned lunar landing.