What is the concept of "Ego" or "self "?

"Me" is a survival instinct, say like the emotion of lust, anger or fear are a survival instinct. Just as anger is a fleeting & passing mood, so is the instinct of 'self'.

For example, the 'self' or 'me' the mind may sense & believe it is today is probably different to the sense & idea of 'self' or 'me' the mind had when it was 3 years old.

Enlightened Buddhists have experienced the dissolution of the 'self' instinct, similar to you may have often experienced the dissolution of an angry mood.

Therefore, to enlightened Buddhists, the 'self' is not a real or permanent 'self'. It is just a mood that arises when the mind is suffering from possessiveness due to lust, anger or fear.

You can read more here: Anatta & Rebirth: Buddhadasa Bhikkhu

The human being is nothing but a collection of five aggregates, a process of complex and rapidly changing (impermanent) psycho-physical organism (nama-rupa), sustained by nutriments, driven by craving in the background of ignorance. But there is a connotation of a “self” in perceiving, feeling, thinking and cognizing that there is a real person, permanent soul or a being in control of it. This false sense of "I" is the Ego.

Ego, in the sense of egotism or selfishness, is a dreadful thing. But the ego in the sense of learning how to function in a way that figures out what is really in your true best interest, and used in a way you’re going to be able to stay on the path, then it is a good thing. In reading The Problem of Egolessness by Thanissaro Bhikkhu you will see the error in our thinking about the ego and understand its harmful effects.

It means that there are various things you might view as yourself (e.g. "I am my body" or "I am my thoughts" or "I am my feelings" etc.), however any and all these views lead to suffering; and that the way to end suffering includes abandoning these views of self (all views of self).

The most famous sutta on the subject is the Anatta-lakkhana Sutta, which says that the body leads to disease, and we can't say "Let my body be this was or not be that way". It says that if the body were self then we'd be able to control it, and that it's because it's not-self that we cannot (and so on for the other aggregates). It's therefore not proper (Pali kalla, also translated skillful, healthy, sound) to consider it self.

My favourite (because I think it's the clearest) sutta on the subject is paragraph 23 of the The Discourse on the Snake Simile -- Alagaddupama Sutta (MN 22) (read the paragraphs before and after this one to get the context):

23. "You may well accept, monks, the assumption of a self-theory[²⁷] from the acceptance of which there would not arise sorrow and lamentation, pain, grief, and despair. (But) do you see, monks, any such assumption of a self-theory?" — "No, Lord." — "Well, monks, I, too, do not see any such assumption of a self-theory from the acceptance of which there would not arise sorrow and lamentation, pain, grief and despair."

There's more for example in MN 2, where it talks about "a thicket of wrong views".

The Buddhist concept is not no self but non self or not self. What this means is there nothing that can be taken as self. There is no permanent unchanging core or soul, there is nothing which you command and control absolutely, there is nothing that an external agency (e.g. God) commands and controls.

Identity view is considering your 5 Aggregates as self, i.e., you consider your body and / or mind as self. In which case if you consider after cutting your hair that this hair is me or a part of me on the floor. The toilet pit is full of me because it was in me at some point. Likewise you should not consider past memories, experiences, thoughts or even your own body as me or mine, because there is no me or mine in the constituting parts, there is no control in any of the parts, each constituent is governed by its own universal law and process which you cannot control.