Recent researchs has proven that the theory of a collision that gave birth to the moon was impossible (there are way too many similar materials between the moon and the earth for the moon to be partially native from an asteroid).
Darwin's grandson placed a theory taking place back when the earth wasn't a "solid planet". It would have spinned so fast that it led to eject some "fluid pieces of earth" outin space, which would have stick together while rotating around the earth, forming today's moon. But once again, that's just a theory.
I have the sources but they are in my native language, so I'll try to look for english ones