The language JavaGI extends Java 1.5 conservatively by a generalized interface mechanism. The generalization subsumes retroactive and type-conditional interface implementations, binary methods, symmetric multiple dispatch, interfaces over families of types, and static interface methods. These features make certain coding patterns redundant, increase the expressiveness of the type system, and permit solutions to extension and integration problems with components in binary form, for which previously several unrelated extensions had been suggested. This article explains JavaGI and motivates its design. Moreover, it formalizes a core calculus for JavaGI and proves type soundness, decidability of typechecking, and determinacy of evaluation. The article also presents the implementation of a JavaGI compiler and an accompanying run-time system. The compiler, based on the Eclipse Compiler for Java, offers mostly modular static typechecking and fully modular code generation. It defers certain well-formedness checks until load time to increase flexibility and to enable full support for dynamic loading. Benchmarks show that the code generated by the compiler offers good performance. Several case studies demonstrate the practical utility of the language and its implementation.