The search for an email, contacts and calendar client for Linux

I’ve been searching for an email client. Well, more than an email client - a piece of software (or interconnected pieces) that can handle email, calendaring and contacts - often referred to as a Personal Information Manager (or PIM). Either natively on Linux, or as a web client. The main reason for this search is that I’m considering moving away from my current mail hoster, Fastmail. Not becau...