Original: Hamas was created in 1987 by Sheikh Ahmed Yassin, Abdel Aziz al-Rantissi and Mohammad Taha of the Palestinian wing of Egypt's Muslim Brotherhood at the beginning of the First Intifada, an uprising against Israeli rule in the Palestinian Territories.
Simplified: It was started in 1987 during the First Intifada  by Ahmed Yassin and Abdel Aziz al-Rantissi as the Gaza branch of the Muslim Brotherhood organziation in Egypt.