In 1871, at the age of eight, Narendranath enrolled at Ishwar Chandra Vidyasagar's Metropolitan Institution, where he went to school until his family moved to Raipur in 1877. In 1879, after his family's return to Calcutta, he was the only student to receive first-division marks in the Presidency College entrance examination.  He was an avid reader in a wide range of subjects, including philosophy, religion, history, social science, art and literature. He was also interested in Hindu scriptures, including the Vedas, the Upanishads, the Bhagavad Gita, the Ramayana, the Mahabharata and the Puranas. Narendra was trained in Indian classical music, and regularly participated in physical exercise, sports and organised activities. Narendra studied Western logic, Western philosophy and European history at the General Assembly's Institution (now known as the Scottish Church College). In 1881 he passed the Fine Arts examination, and completed a Bachelor of Arts degree in 1884. Narendra studied the works of David Hume, Immanuel Kant, Johann Gottlieb Fichte, Baruch Spinoza, Georg W. F. Hegel, Arthur Schopenhauer, Auguste Comte, John Stuart Mill and Charles Darwin. He became fascinated with the evolutionism of Herbert Spencer and corresponded with him, translating Spencer's book Education (1861) into Bengali. While studying Western philosophers, he also learned Sanskrit scriptures and Bengali literature.
William Hastie (principal of Christian College, Calcutta, from where Narendra graduated) wrote, "Narendra is really a genius. I have travelled far and wide but I have never come across a lad of his talents and possibilities, even in German universities, among philosophical students. He is bound to make his mark in life".They probably first met personally in November 1881,[note 1] though Narendra did not consider this their first meeting, and neither man mentioned this meeting later. At this time Narendra was preparing for his upcoming F. A. examination, when Ram Chandra Datta accompanied him to Surendra Nath Mitra's, house where Ramakrishna was invited to deliver a lecture. According to Paranjape, at this meeting Ramakrishna asked young Narendra to sing. Impressed by his singing talent, he asked Narendra to come to Dakshineshwar.
In late 1881 or early 1882, Narendra went to Dakshineswar with two friends and met Ramakrishna. This meeting proved to be a turning point in his life. Although he did not initially accept Ramakrishna as his teacher and rebelled against his ideas, he was attracted by his personality and began to frequently visit him at Dakshineswar. He initially saw Ramakrishna's ecstasies and visions as "mere figments of imagination" and "hallucinations". As a member of Brahmo Samaj, he opposed idol worship, polytheism and Ramakrishna's worship of Kali. He even rejected the Advaita Vedanta of "identity with the absolute" as blasphemy and madness, and often ridiculed the idea. Narendra tested Ramakrishna, who faced his arguments patiently: "Try to see the truth from all angles", he replied.
Narendra's father's sudden death in 1884 left the family bankrupt; creditors began demanding the repayment of loans, and relatives threatened to evict the family from their ancestral home. Narendra, once a son of a well-to-do family, became one of the poorest students in his college. He unsuccessfully tried to find work and questioned God's existence, but found solace in Ramakrishna and his visits to Dakshineswar increased.
One day Narendra requested Ramakrishna to pray to goddess Kali for their family's financial welfare. Ramakrishna suggested him to go to the temple himself and pray. Following Ramakrishna's suggestion, he went to the temple thrice, but failed to pray for any kind of worldly necessities and ultimately prayed for true knowledge and devotion from the goddess. Narendra gradually grew ready to renounce everything for the sake of realising God, and accepted Ramakrishna as his Guru.
In 1885, Ramakrishna developed throat cancer, and was transferred to Calcutta and (later) to a garden house in Cossipore. Narendra and Ramakrishna's other disciples took care of him during his last days, and Narendra's spiritual education continued. At Cossipore, he experienced Nirvikalpa samadhi. Narendra and several other disciples received ochre robes from Ramakrishna, forming his first monastic order. He was taught that service to men was the most effective worship of God. Ramakrishna asked him to care for the other monastic disciples, and in turn asked them to see Narendra as their leader. Ramakrishna died in the early-morning hours of 16 August 1886 in Cossipore.
Narendra was known for his prodigious memory and the ability at speed reading. Several incidents have been given as examples. In a talk, he once quoted verbatim, two or three pages from Pickwick Papers. Another incident that is given is his argument with a Swedish national where he gave reference to some details on Swedish history that the Swede originally disagreed with but later conceded. In another incident with Dr. Paul Deussen's at Kiel in Germany, Vivekananda was going over some poetical work and did not reply when the professor spoke to him. Later, he apologized to Dr. Deussen explaining that he was too absorbed in reading and hence did not hear him. The professor was not satisfied with this explanation but Vivekananda quoted and interpreted verses from the text leaving the professor dumbfounded about his feat of memory. Once, he requested some books written by Sir John Lubbock from a library and returned them the very next day claiming that he had read them. The librarian refused to believe him until cross examination about the contents convinced him that Vivekananda was being truthful.
Some accounts have called Narendra a shrutidhara (a person with a prodigious memory).In 1880 Narendra joined Keshab Chandra Sen's Nava Vidhan, which was established by Sen after meeting Ramakrishna and reconverting from Christianity to Hinduism. Narendra became a member of a Freemasonry lodge "at some point before 1884" and of the Sadharan Brahmo Samaj in his twenties, a breakaway faction of the Brahmo Samaj led by Keshab Chandra Sen and Debendranath Tagore. From 1881 to 1884 he was also active in Sen's Band of Hope, which tried to discourage youths from smoking and drinking.
It was in this cultic milieu that Narendra became acquainted with Western esotericism. His initial beliefs were shaped by Brahmo concepts, which included belief in a formless God and the deprecation of idolatry, and a "streamlined, rationalized, monotheistic theology strongly coloured by a selective and modernistic reading of the Upanisads and of the Vedanta." Rammohan Roy, the founder of the Brahmo Samaj who was strongly influenced by unitarianism, strived toward an universalistic interpretation of Hinduism. His ideas were "altered [...] considerably" by Debendranath Tagore, who had a romantic approach to the development of these new doctrines, and questioned central Hindu beliefs like reincarnation and karma, and rejected the authority of the Vedas. Tagore also brought this "neo-Hinduism" closer in line with western esotericism, a development which was furthered by Keshubchandra Sen. Sen was influenced by transcendentalism, an American philosophical-religious movement strongly connected with unitarianism, which emphasised personal religious experience over mere reasoning and theology. Sen strived to "an accessible, non-renunciatory, everyman type of spirituality", introducing "lay systems of spiritual practice" which can be regarded as prototypes of the kind of Yoga-exercises which Vivekananda popularised in the west.
The same search for direct intuition and understanding can be seen with Vivekananda. Not satisfied with his knowledge of philosophy, Narendra came to "the question which marked the real beginning of his intellectual quest for God." He asked several prominent Calcutta residents if they had come "face to face with God", but none of their answers satisfied him. At this time, Narendra met Debendranath Tagore (the leader of Brahmo Samaj) and asked if he had seen God. Instead of answering his question, Tagore said "My boy, you have the Yogi's eyes." According to Banhatti, it was Ramakrishna who really answered Narendra's question, by saying "Yes, I see Him as I see you, only in an infinitely intenser sense." Nevertheless, Vivekananda was more influenced by the Brahmo Samaj's and its new ideas, than by Ramakrishna. It was Sen's influence who brought Vivekananda fully into contact with western esotericism, and it was also via Sen that he met Ramakrishna.