The Kashiwara's book is quite focused and technical. I won't recommend it as an introduction to sheaves, since the abstract language of sheaves and homological algebra is most useful when you already know **a big class of examples**.

If you're planning on hitting algebraic geometry one day, it could be a good idea to start with reading about it now. Any technical book, e.g. Hartshorne or others suggested in this MO question
will contain such material as sheaves, functors, derived functors, Verdier duality, etc.

There are also better places to learn about D-modules and related stuff; e.g. note Kashiwara's book says:

(p.411) Although perverse sheaves have a short history ...

and, indeed, 30 years later there are quite a few introductions to perverse sheaves that are easier to read.

I don't know about microlocalization, perhaps this topic should be indeed read from Kashiwara.

Now we'll be able to recommend a more specific text if you tell us what exactly you planned on reading Kashiwara for and where you get stuck!

Sheaves on Manifolds", although the book has two authors, Masaki Kashiwara and Pierre Schapira. $\endgroup$ – Pierre-Yves Gaillard Jul 20 '18 at 20:51