Remember myself doing something

What's wrong with:

I remember reading this book [before].

"I remember myself reading this book" sounds like it is grammatically correct to me. It also sounds extremely spacey, as if you've had memory loss of some kind that allows you to recall the act of reading the book without, erm, having any direct memory of having read it.

I remember reading this book, though I can't remember what it was about.

I remember myself reading this- boy, was I suffering.

Inserting the reflexive pronoun myself into “I remember reading this book” shifts the emphasis from the book, and even from the experience of [my] reading the book, towards the self who was doing that reading—with the implication that the speaker has become a different person since that time, but can remember that former personality. This sort of discontinuity over time in one’s personality/identity can be yet more forcefully (perhaps hyperbolically) expressed by referring to the former self in third person, as in A. E. Housman’s Last Poems XXXV:

When first my way to fair I took
   Few pence in purse had I,
And long I used to stand and look
   At things I could not buy.

Now times are altered: If I care
   To buy a thing, I can;
The pence are here and here’s the fair,
   But where’s the lost young man?

Reconstructing OP to more clearly perceive the parameters of this inquiry: “in that sense that I remember how I read the book, is it correct to say: I remember myself reading this book.”

Is it “correct”?

• Grammatically? Yes. Semantically? What are you trying to convey?

• “How” you read the book. If you are remembering the “methodology” you used to read the book, then “how” is the correct word. But if you mean you remember the fact “that” you read the book then you want to say, "I remember that I read the book.” Or, “I remember reading the book.”

• As has already been noted, when you interject “myself” into that otherwise straight-forward and simple sentence you shift emphasis and diffuse meaning. Now emphasis is about the “self” and its experiences (and related associations) while (or, during the span of time in which you were) “reading the book.” In this construction the “memory of reading the book” which I suspect is your point begins to share semantic space with “memory” of the “self.”

• There may be a valid reason for doing such a thing, but what is yours?

I agree with the answer given by @Brian Donovan.

I have a different perspective on the same thing.

In psychological terms, when accessing memory, we have two main options. We can be associated or dissociated.

If we are associated when remembering, we experience the memory as though we are in the same body, seeing and feeling the same things as before.

If we are disassociated when remembering, we see ourselves from the outside and can watch as the action takes place.

Associated: I remember reading this book. (I remember the experience. I re-experience looking at the pages as though I am doing it now)

Dissociated: I remember myself reading this book. (I see myself reading the book in the past. I observe the action from outside my former self)

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As an aside, when associated, most people will re-experience the same emotions as they had before. This may evoke nostalgia for a pleasant event, or fear from a terrifying event. When dissociated, the memory tends to be clinical and without emotion.

For this reason, people who have traumatic experiences often dissociate from the surroundings as a protection mechanism. One form of therapy involves enabling a sufferer to dissociate from a traumatic associated memory.