As a Master student, I learned a lot about arithmetic geometry from blogposts, mathoverflow posts, and random lecture notes - artihmetic geometry is hard, requires lots of background, and these sources usually try to be expository and readable. However, it can be tricky to find and orient in these resources, so I decided to keep a small database (currently under construction) of very useful sources which helped me in the past.
Reductive groups: blogpost coming with a lot of motivation from number theory and very instructive examples.
Formal and p-divisible groups: a blogpost explaining how do p-divisible and formal groups come up in the study of elliptic curves, including the overview of the Serre-Tate theorem.
Scholze's Bourbaki notes: Great introduction into various ideas around the Langlands conjecture. The introduction section is in my opinion very insightful and yet very accessible!
V. Lafforgue's notes: A survey on the Langlands over function fields. What I like about this text is that it explains well how thinking about the Lang isogeny leads to the stack of shtukas! (This was recommended to me by Chenji Fu.)