It's correct usage.
I'm assuming you already know what undergo itself means. The sentence contains a coordination of the complements of "of". It additionally omits any redundant matters that would've been used in the sentence. Then it proceeds to refer to processes with those, having created a mental image of processes beforehand. That's not wrong, that's just good and efficient writing.
This is the unambiguous but cumbersome-to-read version, for comparison:
Chemistry is the study of matter. Chemistry is the study of matter's chemical and physical properties. Chemistry is the study of the chemical and physical changes matter undergoes. Chemistry is the study of the energy changes that accompany the chemical and physical processes.
Finally, the sentence in question boils down to
Chemistry is the study of the chemical and physical changes matter undergoes.
matter undergoes is a relative clause, with an omitted "that". You can think of it as something like I think, syntactically.