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Jamaat-e-Islami (Urdu: جماعتِ اسلامی) is an Islamic political organisation and social conservative movement founded in 1941 in British India by the Islamist theologian and socio-political philosopher, Abul Ala Maududi.
Along with the Muslim Brotherhood, founded in 1928, Jamaat-e-Islami was one of the original and most influential Islamist organisations, and the first of its kind to develop "an ideology based on the modern revolutionary conception of Islam".
The group split into separate independent organisations in India and Pakistan -- Jamaat-e-Islami Pakistan and Jamaat-e-Islami Hind—following the Partition of India in 1947. Other groups related to or inspired by Jamaat-e-Islami developed in Bangladesh, Kashmir, Britain, and Afghanistan (see below). The Jamaat-e-Islami parties maintain ties internationally with other Muslim groups.
Maududi was the creator and leader of the militant Jamaat-e-Islami, which became the spearhead of the movement to transform Pakistan from a Muslim homeland into an Islamic state. Though he opposed the creation of Paksitan fearing the liberalism of its founders and the British-trained administrators, he later accepted it as a graudual step to the Islamization of its laws and constitution even though he had earlier condemned the Muslim League for the same approach. Madudi like the traditionalist ulama regarded the six canonical hadiths and the Quran, and also accepted much of the dogma of the four schools of fiqh. His efforts focused on transforming to a "theo-democracy" based on the Sharia which would enforce things like abolition of interest-bearing banks, sexual separation, veiling of women, hadd penalties for theft, adultery, and other crimes.  The promotion of Islamic state by Maududi and Jamaat-e Islami had broad popular support.
Maududi created Jamaat-e-Islami with the objective of making post-colonial India (or a separate Muslim state if the Muslim League got its wish), an Islamic state. Although this would be the result of an "Islamic revolution", the revolution was to be achieved not through a mass organising or a popular uprising but by what he called "Islamization from above", by winning over society's leaders through education and propaganda, and through putting the right people (Jamaat-e-Islami members) in positions of power. incrementally and through legal means.
Mawdudi believed politics was "an integral, inseparable part of the Islamic faith". Islamic ideology and non-Islamic ideologies (such as capitalism and socialism, liberalism or secularism) were mutually exclusive. The creation of an Islamic state would be not only be an act of piety but would be a cure for all of the many (seemingly non-religious) social and economic problems that Muslims faced. Those working for an Islamic state would not stop at India or Pakistan but would effect a sweeping revolution among mankind, and control all aspects of the world's life.
Maududi opposed British rule but also opposed both the anti-colonialist Muslim nationalist Muslim League's proposal for a separate Muslim state led by Muhammad Ali Jinnah, and the "composite nationalism" (muttahida qaumiyyat) idea of Jam'iyyat al-Ulama-ye Hind and Deobandi scholar Husain Ahmad Madani for a united independent India with separate institutional structures for Hindus and Muslims.
Although Maududi believed Muslims formed a separate nation from the Hindus of India, he initially opposed the partition of India to create a "Muslim state" circumscribed to Muslim-majority regions, agitating instead for an "Islamic state" covering the whole of India—this despite the fact Muslims made up only about one quarter of India's population.
In his view Muslims were not one religious or communal group among many working to advance their social and economic interests, but a group `based upon principles and upon a theory` or ideology. A "righteous" party (or community) that had "a clearly defined ideology, allegiance to a single leader, obedience, and discipline", would be able to transform the whole of India into Dar al-Islam. Unlike the fascists and communists, once in power an Islamic state would not be oppressive or tyrannical, but instead just and benevolent to all, because its ideology was based on God's commands. 
In 1940, the Muslim League met in Lahore and passed the Pakistan Resolution, calling for autonomous states in the Muslim majority areas of India. Maududi believed the nationalism in any form was un-Islamic, concerned with mundane interests of people and not Islam. In response he launched his own party, Jamaat-e-Islami, founded on 26 August 1941, at Islamia Park, Lahore. Seventy-five people attended the first meeting and became the first 75 members of the movement.
Maududi saw his group as a vanguard of Islamic revolution following the footsteps of early Muslims who gathered in Medina to found the first "Islamic state". Members uttered the Shahada, the traditional statement of conversion to Islam, when they joined, implying to some that Jama'ati felt they had been less-than-true Muslims before joining. Jamaat-e-Islami was and is strictly and hierarchically organised in a pyramid-like structure. All supporters work toward the common goal of establishing an ideological Islamic society, particularly through educational and social work, under the leadership of the emir. Being a vanguard party, not all supporters could be members, only the elite. Below members were/are "affiliates", and "sympathizers" beneath them. The party leader is called an ameer (commander).
Maududi sought to educate the elite of the Muslim community in the principles of Islam and correct "their erroneous ways of thinking" both because he believed societies were influenced from the top down.
During the years before the partition of India, Jamaat-e-Islami stood aloof from the intense political fights of the time in India, concentrating on "training and organising" and refining and strengthening the structure of Jamaat-e-Islami.