During the last days of Sri Ramakrishna a group of young men had gathered round him and began to nurse him, as he was ill seriously, while receiving spiritual guidance from him. Narendranath, later world widely known as Swami Vivekananda (1863-1902), was the leader of this group. Ramakrishna had wanted them to lead a monastic life. In 1886, shortly after the passing away of Sri Ramakrishna, a monastic order bearing his name was organized in pursuance of his own instructions, with a monastery at Baranagar, a northern suburb of Kolkata, by his Sannyasin disciples headed by Narendranath. They began to live together, depending upon what they got by begging. Thus the “Ramakrishna Math” had come into the existence

Old Baranagar Math 
Gradually, it set for itself a two-fold ideal: To create a band of Sannyasin teachers of Vedanta as propounded by Sri Ramakrishna and practically illustrated his own life; and To carry on missionary and philanthropic works, in conjunction with lay devotees, looking up on all, irrespective of caste, creed, or colour, as veritable manifestations of the Divine. Later Narendanath became the famous Swami Vivekananda and spread to the western world the message of spirituality and principles of Vedanta. After his returning home from his memorable visit in the West, in order to materialize his Guru’s instructions, he founded the “Ramakrishna Mission” in Kolkata on 1 May, 1897.
The Ramakrishna Math was registered as a trust in 1901. To facilitate the work of the Mission Association and for giving it a legal status, a society named the Ramakrishna Mission was registered in 1909. Thus  the twin organizations of Ramakrishna Math and Ramakrishna Mission, form the core of a worldwide spiritual movement—the Ramakrishna Movement or Vedanta Movement, and aims at the harmony of religions, harmony of the East and the West, spiritual fulfillment, social equality, and peace for all humanity,  amongst other things, without any discrimination or distinctions of creed, caste, race or nationality.
One ideal of the organization is: “To preach those truths which Sri Ramakrishna has, for the good of humanity, preached and demonstrated by practical application in his own life, and to help others to put these truths into practice in their lives for their temporal, mental, and spiritual advancement.”

The headquarters of the worldwide twin organizations are situated on the serene campus of Belur Math on the Ganga, which includes temples dedicated to Sri Ramakrishna, Sri Sarada Devi and Swami Vivekananda, in which their relics are enshrined, and the main monastery of the Ramakrishna Order.  The place has been sanctified by the stay of Swami Vivekananda and many of the monastic disciples of Sri Ramakrishna who spent several years there.  Holy Mother Sri Sarada Devi also visited the place on several occasions.  
The Math and the Mission together have 176 other branch centres all over India and in different parts of the world. All branch centres of Ramakrishna Math come under the administrative control of the Board of Trustees, whereas all branch centres of Ramakrishna Mission come under the administrative control of the Governing Body of Ramakrishna Mission. 

Those branches of the Ramakrishna Order located outside India are generally known as Vedanta Societies, and are under the spiritual guidance of the Ramakrishna Order. The work of the Vedanta Societies in the West has primarily been devoted to spiritual and pastoral activities, though many of them do some form of social service.
On the Indian subcontinent, the Ramakrishna Mission has been in the forefront of philanthropic activities. Its first social service efforts—inspired by Swami Vivekananda—began in 1897. Since that time, the Mission’s activities have continued to expand up to the present day.
The Ramakrishna Mission has its own hospitals, charitable dispensaries, maternity clinics, tuberculosis clinics, and mobile dispensaries. It also maintains training centers for nurses. Orphanages and homes for the elderly are included in the Mission’s field of activities, along with rural and tribal welfare work.
In educational activities, the Ramakrishna Mission has consistently been ahead of its time. It has developed some of the most outstanding educational institutions in India, having its own colleges, vocational training centers, high schools and primary schools, teachers’ training institutes, as well as schools for the visually handicapped. It also has adult education centers through out the county.
Whenever disaster has struck, the Ramakrishna Mission has been there to offer relief from famine, epidemic, fire, flood, earthquake, cyclone, and communal disturbances.