In recent years applied mathematics has experienced a historical progress, blurring the lines between the previously clear research paths and directions. Accordingly, contemporary mathematical analysis is at the verge of unifying seemingly different research areas and topics. With this in mind, I’d like to talk about my humble contribution to this cause: my lecture will concern how Banach algerbas and modules, combined with spectral theory, functional calculus, and generalized inverses, help in various problems that emerge in applied mathematics in general: from solving operator and matrix equations, to evaluating sums of some Banach-space-valued series, to analyzing some unstable abstract Cauchy problems, and finally to approximating solutions to functional stochastic differential equations.