。
Once I've finished reading the book, I'll return it on Tuesday.
Literal
Book [object-を] read-[completion-てしまう]-[if-たら] Tuesday [on-に] [humble-お] return-do-[polite].
Three layered structures. ~てしまう + たら = 'once/when one has completed X' — the completive ~てしまう combined with the たら conditional creates 'once done.' お返しします is humble polite: お + 返し (stem of 返す) + する creates the humble-action pattern お~する, used for the speaker's own actions when speaking to a superior or customer. Note that 'next Tuesday' is simply 火曜日に; Japanese doesn't always specify 'next.'