Jihad is “a religious war with those who are unbelievers in the mission of the Prophet Muhammad [the Prophet]. It is an incumbent religious duty, established in the Qur’an and in the Traditions as a divine institution, and enjoined specially for the purpose of advancing Islam and repelling evil from Muslims" (T.Hughes, Dictionary of Islam, entry “Jihad” ).
Shorter Encyclopaedia of Islam, page 89, :
DJIHAD, holy war. The spread of Islam by arms is a religious duty upon Muslims in general. It narrowly escaped being a sixth “rukn”, or fundamental duty, and is indeed still so regarded by the descendants of the Kharidjis. The position was reached gradually but quickly. In the Meccan Suras of the Kur’an patience under attack is taught; no other attitude was possible. But at Madina the right to repel attack appears, and gradually it became a prescribed duty to fight against and subdue the hostile Meccans. Whether Muhammad himself recognized that his position implied steady and unprovoked war against the unbelieving world until it was subdued to Islam may be in doubt. Traditions are explicit on the point; but the Kuranic passages speak always of the unbelievers who are to be subdued as dangerous or faithless. Still, the story of his writing to the powers around him shows that such a universal position was implicit in his mind, and it certainly developed immediately after his death, when the Muslim armies advanced out of Arabia. It is now a “fard ‘ala ‘l-kifaya, a duty in general on all male, free, adult Muslims, sane in mind and body and having means enough to reach the Muslim army, yet not a duty necessarily incumbent on every individual but sufficiently performed when done by a certain number. So it must continue to be done until the whole world is under the rule of Islam.”