According to Buddhism there is no 'I'. Our sense of self is an illusion based on faulty perception. An individual is no more than the combination of the five skandhas or aggregates of existence which can be summarised as 1) the physical form, 2) the emotions and sensations, 3) thinking and conceptualising, 4) habits, prejudices and will (grouped together as psychological formations), and 5) consciousness as reaction to the six external objects which are those associated with the five senses and the mind. These are regarded as empty, using the classic Buddhist term, in that there is nothing real (as in an individual) behind them. Rather it is they that create that idea. Buddhism is not nihilistic because it says that there is a reality beyond this (that's the whole point of it, of course) but the individual has no part in this reality.
This is very good theory and sounds intellectually rigorous enough to be true but it is not true, not the complete truth anyway. Where our individuality is concerned, the whole is not just the sum of the parts. There is an individual soul and that is not an illusion. It was created, so it cannot perhaps be said to be more than relatively real, but it is not unreal. Ultimately, of course, there is only God or the Unborn, Unmade and Uncompounded, if you prefer to think of it in those terms, but existence is not made up of the absolute alone. It is a combination of the absolute and the relative, and the two together make the whole. You cannot deny either one of them, even if you must see the relative as an aspect of the absolute and not real in its own right.
What this means is the following. Out of the Unmanifest Absolute comes the creator God who creates the manifest universe out of his own being. Why? Hinduism calls this his play (lila), Islam says that God was an unknown treasure and desired to be known. I would say that either there is no reason, it is just what is (if something is possible then it must be); or, less unhelpfully, that God desired to become more which he could only do by creating self-conscious individuals, that’s to say, multiplying himself; or again, that it is only through manifestation that there can be love, beauty and joy. So God created individual souls in order to achieve these things. They are real. You are real. But (and here is the critical point and one on which the Buddhist position is correct), you are only relatively real. Your goal is to outgrow your identification with the limited, individual self and realise yourself to be the Universal Self. But that does not mean that the dewdrop slips into the shining sea and is no more because if it did then what would be the point of creation? Identification with self is transcended but its quality remains as, unless we are to disappear into pure formlessness and no longer be, it must. It is seen in an entirely different light and is no longer the centre of our being but it remains as our expressed self. You might think of the realised soul as Janus-like in that it looks two ways, inwards to the absolute where there is no self or rather One Self, but outwards too where the individual still exists as a particular expression of the absolute, its focus on a unique point.
In the book Towards the Mysteries the Masters make the following statement. God made man Individual.
I have no desire to get caught up in theorising about ultimate reality but I do think it important to get at the truth, and that is why I reject the Buddhist doctrine that self is an illusion. It is very possible that more souls have reached enlightenment through Buddhism in the past than any other way, but the introduction of Buddhist thought to the Western mentality is not without its problems, and the main one is the misapplying of ideas that relate to the plane of the absolute to the relative plane.
In a nutshell, I think there is confusion in Buddhism between the ego and the individual. The ego is an illusion born of identification with the mind. It is our creation. But the individual soul is the creation of God. God multiplied Himself to become More, this was why He created. Yes, in absolute terms there are no individual selves and we must come to realise our identity with that primordial state but, until the universe slips back into non-being, the so called Night of Brahma, the absolute is not all there is. Maya exists. It must be seen through, and we should not be bound by it (which is our current condition), but it cannot be denied.
If there is no self then who attains Nirvana? You might say that the realisation of the non-existence of the self is Nirvana but then you also have to ask what realises this non-existence? In one sense it is, of course, the Self realising the Self as, ultimately speaking, that is all that can ever be, but the Self knows itself eternally anyway. In terms of this realisation, it is a specific individual that has realised its oneness with the universal Self, and that individual is now for the first time truly undivided which, after all, is what individual actually means.
We are made in the image of God. God has individuality and so do we. There may be something beyond this but that does not mean that it is not real.