Swami Vivekananda, born as Narendranath Datta, was a prominent disciple of Sri Ramakrishna and a key figure in the revival of Vedanta philosophy in India. After the passing of his guru, Swami Vivekananda played a crucial role in the establishment of the Ramakrishna Math and Mission, which has since become a renowned spiritual and humanitarian organization.

As a disciple of Sri Ramakrishna, Swami Vivekananda was deeply influenced by his guru's teachings and philosophy. He saw the need for a spiritual organization that would spread the message of Vedanta and serve the society, and thus, the idea of Ramakrishna Math and Mission was born. Swami Vivekananda believed that the teachings of Sri Ramakrishna were not just for a select few but for the entire world, and he wanted to make them accessible to all.

In 1886, Swami Vivekananda and a group of his fellow disciples started a small monastery at Baranagar, which served as the first center of the Ramakrishna Math. However, it was not until 1897 that the formal establishment of the Ramakrishna Math and Mission took place. Swami Vivekananda, along with his brother disciples, Swami Brahmananda, Swami Premananda, and Swami Yogananda, worked tirelessly to set up the organization and its various branches.

One of the significant contributions of Swami Vivekananda towards the establishment of the Ramakrishna Math and Mission was his fundraising efforts. He traveled extensively, both in India and abroad, giving lectures and talks on Vedanta and the teachings of Sri Ramakrishna. He also met with influential people and sought their support for the mission. His efforts were successful, and he was able to raise enough funds to purchase a large piece of land on the western bank of the Ganges in Belur, West Bengal, where the headquarters of the organization, the Belur Math, stands today.

Apart from fundraising, Swami Vivekananda also played a critical role in shaping the ideology and structure of the Ramakrishna Math and Mission. He emphasized the importance of selfless service and encouraged the monks to engage in various social welfare activities. He also introduced the concept of the 'Sannyasa Order,' which allowed monks to serve the society while living a life of renunciation.

In conclusion, Swami Vivekananda's role in the establishment of the Ramakrishna Math and Mission was crucial. His unwavering dedication, visionary leadership, and tireless efforts were instrumental in making the organization what it is today. His teachings continue to inspire and guide the members of the Ramakrishna Math and Mission, as well as millions of people around the world, to lead a life of service, love, and spiritual growth.