This paper presents a novel adaptive control methodology for uncertain systems with time-varying unknown parameters and time-varying bounded disturbances. The adaptive controller ensures uniformly bounded transient and asymptotic tracking for both the system's input and output signals, simultaneously. The performance bounds can be systematically improved by increasing the adaptation gain. Robustness of the L-1 adaptive controller to non-zero trajectory initialization error is addressed. Simulations of a robotic arm with time-varying friction verify the theoretical findings.