Sheikh `Umar al-Muqbil, professor at al-Imâm University
Ahmad had numerous teachers, too many to be mentioned in this short answer. Many of them are discussed by al-Hâfiz al-Mizzî in his book Tahdhîb al-Kamâl (1/437).
Some of his most famous teachers were Imam al-Shâfi`î, Abû Dâwûd al-Tayâlîsî, Muhammad b. Ja`far (known as Ghandar), Sufyân b. `Uyaynah, Muhammad b. Hâzim al-Darîr (known as Abû Mu`âwiyah), Wakî` b. al-Jarrâh, `Abd al-Razzâq b. Hammâm al-San`ânî (the author of al-Musannaf), al-Walîd b. Muslim, `Affân b. Muslim, Ismâ`îl b. `Aliyyah, and Aswad b. `Amir (known as Shâdhân). The list goes on.
Some of his most eminent students were: al-Bukhârî, Muslim, Abû Dâwûd (the author of al-Sunan), Ahmad’s own sons `Abd Allah and Sâlih, his cousin Hanbal b. Ishâq, Abû Hâtm al-Râzî, Abu Zur`ah al-Râzî, and Yahyâ b. Ma`în. All of these famous people were leading scholars of hadîth.
In talking about how the Hanbalî school of thought developed, it has its start when Ahmad b. Hanbal became famous, particularly after he underwent his great ordeal for insisting that the Qur’ân was not created.
Ahmad was steadfast on his opinion. He was jailed, tortured, and nearly killed for it. People came to love him and hold him in high esteem. Students came to him from all over the world.
Ahmad b. Hanbal was extremely keen on recording, criticizing, and transmitting hadîth. This is why he never wrote a book in the field of Islamic Law, as you have pointed out in your question.
(With respect to his hadith work al-Musnad, the best and most complete edition in print, published by Muassasah al-Risâlah, contains 27,647 hadîth.)
After Ahmad's death, his students gathered together and wrote down the answers that they had received from the many questions on Islamic Law that they had asked him. The compliation of these answers continued at the hands of their students. This corpus of knowledge increased gradually until it formed the Hanbalî school of thought.
Hanbalî books have made a rich contribution to the field of Islamic Law, as have the works of the other three schools of thought.
Source: Islam Today