Summary of contents: densely defined and adjoint operators, proof of well-definedness; adjoint of sum; kernel and range (or image) of an operator; injective, surjective, and invertible operators; ker(A^*) = ran(A)^perp; extension of an operator; relation between extensions and adjoints; symmetric operators; remark on Hermitian operators; self-adjoint operators and self-adjoint extensions; closable operators; closure of an operator; closed operators; a symmetric operator is necessarily closable; essentially self-adjoint operators; unique self-adjoint extension; defect indices; criteria for self-adjointness and essential self-adjointness without calculating the adjoint; proofs and examples.
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