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Literally, Vedanta means the end or the concluding portion of the Vedas and the universal philosophy of Vedas is succinctly summarized in the Vedanta. It is one of the world’s most ancient religious philosophies and one of the broadest. Vedanta affirms the oneness of existence, the divinity of the soul, and the harmony of religions. Vedanta is the philosophical foundation of Hinduism; but while Hinduism includes aspects of Indian culture, Vedanta is universal in its application and is equally relevant to all countries, all cultures, and all religious backgrounds.

The idea of harmony of religions is expressed in one of the earliest Vedantic texts — ekam sat viprā bahudhā vadanti (“Truth is one, sages call it by var­i­ous names”) (Rig Veda). Vedanta holds that different spiritual schools of thought while superficially appearing to point differently, after a shorter or longer journey, will ultimately reach the Supreme if one pursues any school with perseverance. This is analogous to different rivers flowing in different directions reach the ocean.

To whatever school one may belong, one ought not to linger or stop on the way. Vedanta recognizes that all paths lead to the same goal, and obviates the necessity to change the path one is already following. Consequently, there is also no room for hatred towards a person following a different path. The place of worship, the worshiped, and the form of worship, all these three may differ for different people, due to difference in taste. But what is required of one is to persist in the path one is following.

Yoga

The spiritual path, according to Vedanta is called Yoga (This is different from the popular interpretation of yoga as physical exercise). It can be broadly classified into four types of paths. An aspirant can choose one or more of these paths for his/her spiritual journey, based on his/her nature, inclination and personality. These four types of paths are:

Karma Yoga or the 'Yoga of Work' is the path of unselfish work, renouncing the results of one's actions as an offering, rather than hoarding the results for oneself. If any work is done, good or bad, it must produce good or bad Karma as a result. Good karma creates non-attachment; destroying the tendency towards bad Karma and purifying the mind. On the other hand, if the work is done with the intention of enjoyment, it then produces only that very enjoyment and does not purify the mind. Karma Yoga is the state in which all work is done without any desire to enjoy the fruits of the work. Such work without desire of return will destroy the selfishness, which is the root of all bondage. It manifests the natural divinity in all, making one love all sacrifice simply for the good of others, without any ulterior motive, irrespective of one's position in society.

Bhakti Yoga or the 'Yoga of Love/Devotion' is one of the most popular paths found in many religions because it is the easiest, most endearing and natural way of humans. Love is the natural impetus of union in the human heart. Love, when properly directed towards the proper object can bring deliverance. That object as prescribed by Bhakti Yoga is God. Love cannot be without a subject and an object. The object of love again must be at first a being who can reciprocate our love. Therefore the God that one loves must be in some sense a human God. Aside from the question whether such a God exists or not, it is a fact that to those who have love in their heart, the Absolute appears as a personal loving God. Forms of worship, which embody the idea of God as a judge or punisher or someone to be obeyed through fear are superseded by the worship of God through love.

Raja Yoga or the 'Yoga of Meditation' fits in with every one of the other Yogas. Raja Yoga details the use of the strength of one's mind to realize the Truth. The basic premise of raja yoga is that the perception of the divine is obscured by the disturbances of the mind. If that mind can be made still and pure, the divinity will automatically, instantaneously, shine forth. As such, Raja Yoga fits inquirers of all classes with or without any belief. Pranayama (breathing exercises), concentration, meditation and chanting are a few types of activities undertaken by aspirants of Raja Yoga.

Jnana Yoga is the 'Yoga of Knowledge or Philosophical Discrimination'. This is the knowledge of the Self and God. Where the Bhakta follows the promptings of the heart, the Jnani uses the power of reasoning to discriminate between the real and the unreal, the permanent and the transitory. The seekers strive to discover the Self within, through the power of rea­son, by cast­ing off the false super­im­po­si­tion of the body, mind, senses, intel­lect, and person­al­ity. As a result of this prac­tice, the seeker real­izes the Supreme Real­ity to be present within as one's own higher Self, and knows one­self to be the birth­less, death­less Real­ity. There are three parts in this path. First: hearing the truth, — that the Atman (Soul) is the only reality and that everything else is Mâyâ (relativity). Second: reasoning upon this philosophy from all points of view. Third: giving up all further argumentation and realizing the truth.

Swami Vivekananda summarizes the four-fold path of yoga as "Each soul is potentially divine. The goal is to manifest this divinity within, by controlling nature, external and internal. Do this either by work, or worship, or psychic control, or philosophy— by one or more or all of these— and be free. This is the whole of religion. Doctrines, or dogmas, or rituals, or books, or temples, or forms are but secondary details."

For a more detailed explanation about Vedanta and the four yogas see here.

Swami Vivekananda's lectures on the four yogas are spread through volumes 1,2 and 3 of his complete works which are available online here.