Gamut is certainly a good entry point, but is already quite dated and not that mathematical. After Gamut I'd recommend Partee et al. 'Mathematical Methods in Linguistics', which gives you some background in algebra and formal language theory. More mathematical ground is explored in Markus Kracht's 'The Mathematics of Language', but is quite hard going. Then you might try some additional textbooks: Heim and Kratzer's 'Semantics in Generative Grammar' and its intensional companion 'Intensional Semantics' by Kai von Fintel use generative grammar as the syntactic basis, which is not everyone's taste. Textbooks using categorial grammars (which are a kind of linear logic) include Pauline Jacobson's 'Compositional Semantics' and Bob Carpenter's 'Type logical Semantics'.
After that you might start reading the original works and / or try out some handbook articles: Many classics are collected in the volume 'Formal Semantics: The Essential Readings'. Frank Veltman's homepage also has a nice list of memorable works in semantics. Good handbooks include 'The Handbook of Logic and Language', 'The Handbook of Contemporary Semantic Theory' and 'Semantics: An International Handbook of Natural Language Meaning'.
Have fun with semantics and bon voyage.