Both Buddhism and Advaita Vedanta are both powerful ancient traditions . , full of important insights and guidance . Teachings of Buddha are similar to the teachings of many rishis and the ancient sages who composed the earliest Hindu scriptures . The relationship between Hinduism and Buddhism is bit complicated . All hindus look upon Buddha as a religious reformer , a free thinker and who rejected Hinduism 's excessive ritualism of that time and reinvigorated it with new teachings . In some Hindu scriptures Buddha is accepted as an avatara , i.e., ninth  avatara of lord vishnu . But , Buddha rejected the authorities of all Hindu scriptures . He is the founder of a new religion which is rooted in Hinduism , but distinct from it. 

The fact is Buddha himself was raised in a Hindu family and learned from hindu teachers .

  Both hinduism and buddhism impart various beliefs , beliefs about , heaven and hell and how the universe is created . The meaning of vedanta is the spiritual knowledge that we get from upanishad .The source of spiritual knowledge called upanishads . Some teachings of hinduism are found in vedas and upanishads and the same teachings are found in Sutras , the texts that contain the discourses of buddha . The foundation of buddha is based on four noble truths —-

1 — the truth of dukha , suffering 

2 —-the suffering has specific causes like craving , aversion and ignorance. 

3——this suffering can be eliminating its specific causes 

4——path and practices by which you can eliminate those causes and become can be from suffering .

These four noble truths are similar to the vedanta's main concept which says that suffering is the result of craving and aversion , which are themselves the result of ignorance. By removing the ignorance , we can be free from sufferings .The teachings of Buddha and the ancient rishis are very much alike . Both the help to eliminate the false identification with your body and  

mind and free you from suffering . Buddha rejected both the extreme positions of Being  and Non -Being . He preached the doctrine that embodied the middle mode of becoming ; believing neither in chance nor in necesiity exclusively , but in conditioned happening . Here , he was not only putiing forward his concept of the law of causation but was also pointing to the principle of identity at each stage. 

 

Buddhism and Advaita Vedanta are different fingers pointing at the moon . The purpose in each case is the same .We have to select the path we prefer . . But , the intellectual explanation and conceptual thinking keep us focussed on the finger . .Huang Po , Guru Rinpche and Ramana remind us of this . 

Both the teachings of buddhism and advaita vedanta , will elilminate the false identification with the body and mind and free from suffering . Both traditions address and solve the fundamental problem of human suffering ,  but they differ on the existence or non -existence of a true , inner self , atma. The cause of suffering to be desire, karma , or Trisha , and identify enliglightment , moksha or nirvana , to be the result becoming free from desire . But , buddhism teaches that freedom from desire is gained by understanding the impermanence of the world , samsara and the metaphusical abscence of an individual person , soul or atma , that is subject to suffering . Advaita vedanta addresses the problem of desire by leading one to discover the true self , atma .Both the traditions seek to eradicate ignorance , ajnana . 

Acharya  Shri Shankaracharya , of 8th century , relied on experience , common as well as extraordinary to build his theory of brahaman , I .e., Advaita . He gave credence to an individual's subjective experience. He placed personal experience and intutition above all the other means of cognition . He said a person's experience could not be disputed . He declared , " Intution is not opposed to intellect . Reality is experience. Realizing the supreme being is within ones experience " . He also said it is not an intellectual construct but a matter of experience , which wiil make us to do all the time. .Thus , an idividual experiences the world through his senses , mind & other ways of perception . Vedanta of Sri Sankara comes as a remedy to the conflict and voilence ridden ways of our life. Swami Vivekananda aptly described Sri Sankara's Advaita as the fairest flower of philosophy that any country in age in any age can follow it. 

Sri Sankara's dispute with the Buddhist schools { Madhyamika & Vaibhasika ] was purely metaphysical and not religious . By this time Buddhism had moved closer to Upanishads and the chasm between Vedanta and Buddhism had narrowed a great deal.