In many applications, it is desirable to control interfacial properties by employing adsorbed polymer layers, In this work, we study the adsorption of random heteropolymers and find a rich surface phase diagram that suggest ways in which the properties of the adsorbed layers can be controlled rather precisely by manipulating the physical conditions. Specifically, we present a comprehensive field-theoretic analysis of the surface phase diagram of a solution of random heteropolymers interacting with a chemically homogeneous solid surface, and find many surface transitions that may be exploited in applications. The different types of polymer segments interact with the solid surface in arbitrarily different ways. Our analysis, wherein a replica method is employed to average over the quenched sequence fluctuations, allows us to obtain the surface free energy functionals that show that our problem partially resembles a semi-infinite Ising spin system. Thus, akin to the Ising system, the phase diagram exhibits exotic surface transitions. In the infinitely dilute limit we find four "massless" transition lines : the ordinary (OT), the surface (ST), the extraordinary (ET), and the special (SPT) transition. At finite bulk solution concentration, we find two transitions : viz. the OT and the adsorption-depletion (ADT) transitions. The nature of the critical points that reside on the transition lines are analyzed, and the physical meaning of each of the surface transitions is elucidated, Our results are related to experiments and it is shown that the interesting behavior that random heteropolymers exhibit near surfaces is due to the quenched sequence fluctuations.