In the US, tenure-track (TT) positions seem a common and natural step in the progression towards an academic career and quite "stable" state-wise in terms of what one might expect from them, in that if nothing goes too wrongly, after the fixed X years in a TT position one can reasonably expect to get tenure (I've heard of horror stories of denied tenure from certain R1 universities, but I'm more concerned about the generic case here).
Now, I'm in the early stages of my academic career (I'm soon to start my first postdoc) and, more relevantly for the purposes of this question, I'm based in Europe and, unless I have absolutely no other options, I intend to remain in Europe in the future. My understanding of what the "natural" steps to take after the postdoc phase in Europe is, admittedly, pretty muddy and quite scattered.
My question(s) is (are):
Is there an equivalent (step-wise in the progression towards an academic career) in Europe of the tenure-track positions in the US? If so, is this equivalent step "stable" country-wise, or does it change considerably depending on the country? More generally, what is the "natural" progression in Europe after the postdoc phase?
Sorry for the many questions, but most of the advice I usually find is very US-centric.
EDIT: To make the question a bit more specific, I'm particularly interested in France, UK, Italy, and Germany. Also, I'm trying to pursue an academic career in mathematics, so I'm also interested in those aspects specific to the discipline, if there are any such.