A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum mechanical description is obtained in the idealized case of measurements of infinitely short duration. A theory of perturbation is developped. As a sample application Fermi's Golden Rule and the S-matrix are derived. The theory also offers a solution to the controversal issue of the time-energy uncertainty relation.