The BEST book of measure theory for beginners

I suggest Measure theory, by Donald L. Cohn.

Here are $\textbf{3}$.

$\bullet$ Real analysis for graduate students by Richard F. Bass

$\bullet$ Royden, $3$rd or $4$th

$\bullet$ M.T (https://www.ndsu.edu/pubweb/~comez/Lecture%20Notes%20and%20Talks.htm)

The second are notes from a professor at my university. They worked really well for me when studying for my qualifying exams. I provided the first reading because it goes into more detail and has a similar style. The middle I used a lot as well. Most measure theory notes that you will find, if free, differ by a very small amount. So almost every set will have everything you need, its just a matter of finding the right style.

I'm surprised that no one mentionned the famous Rudin's book : Real and Complex Analysis. As a student, it really helped me. Moreover, at the end of each chapter there is an historical note on the subject we just studied. Really interesting and helpful.