The perimysium is the connective tissue sheath around fascicles of muscle.
The periosteum is the connective tissue covering of a bone.
The perichondrium is the connective tissue which surrounds cartilage.
The perineurium is the covering of nerve fascicles.
The endosteum is the lining of the inner bone (the side which abuts the medullary cavity).
Note from Sarah Bellham: The prefix "peri" means around, such as in the word "perimeter". The prefix "endo" means within or inner, such as in "endosteum", "endocrine", "endoscope".