Who is the first female president in the world?

Isabel Martinez de Peron of Argentina was the first woman to have the office of National President; she suceeded her husband President Juan Peron on his death on July 1, 1974 and was deposed in a coup on March 24, 1976.
Khertek Amyrbitovna Anchimaa-Toka was a Tuvan/Soviet politician who in 1940-44 was a chairwoman of Little Khural (parliament) of Tuvan People's Republic, and the first elected or appointed (i.e., not hereditary) female head of state in the modern world.

Isabel Martínez de Perón of Argentina was the first female president in the world, where the position was called president.
Isabel Peron was the first female president in the world. She was president of Argentina from 1st of July 1974 to 24th of March 1976.
There have been many, many female heads of state (historically queens and empresses), from Cleopatra to Queen Elizabeth I. Women who have held a title of "president" include:

Khertek Achimaa-Toka served briefly as the president of the short-lived People's Republic of Tannu Tuva from 1940-1944.

Suhbaataryn Yanjmaa served as acting president of Mongolia from 1953 to 1954.

Sirimavo Bandaranayaka of Sri Lanka (Dominion of Ceylon) was the first lady Prime Minister in the world (1960-65, 1970-77 and 1994-2000). Her daughter Chandrika Bandaranayaka Kumaratunga (CBK) was the 4th President of Sri Lanka from 1994 to 2005.

Song Qingling served as acting head of state of Chinafrom 1968 to 1972.

Maria Estella Martinez Cartas "Isabel" de Peron of Argentina was the first woman to hold a "nonprovisional" presidency of a "nonprovisional" government when she served as president from 1974 to 1976, succeeding her husband Juan Peron.