An Introduction to Quantum Computation and Quantum Communication (2000) [pdf]
herpolhode.com
herpolhode.com
Obviously any introduction from the early aughts is going to be noticeably out of date compared to the current state of the art. But since the core fundamentals remain the same it's still a very good place to begin learning about the subject. It's also good reading to gain some perspective of what the cutting edge looked like at the turn of the century.
In particular, de Wolf's work lays out a cursory introduction to quantum mechanics before giving a walkthrough of several early quantum algorithms (Deutsch-Jozsa, Bernstein-Vazirani, Simon, Grover, Shor). Then he moves on to fundamental quantum computing and complexity theory, and finally to quantum communication. An appendix gives a refresher to the linear algebra you'll need to follow along (i.e. you should have familiarity with linear algebra before reading this, but you don't need to be adept with tensor analysis).
If you'd like a more recent and accessible (if not as complete) introduction to the subject, de Wolf also published the lecture notes for the graduate course[2] he taught in 2011. This has been continually updated with errata and additions through 2018. The lecture notes for this course largely take the survey material from his dissertation and build upon them with research results from the past 17 years.
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