Social skills aren't really something you can learn from a book. It would be much more helpful to check out criteria for AS and case studies about it and see what aspects of it you identify with. This is so you'll learn the specific ways that AS affects you and what you need to work on. The reason I say this is that AS presents differently in every person, and so we'll each have different things to improve on. This was my first step into developing my social skills, and I gained a lot of self-awareness.
The second step after this is to practice, practice, practice. It's one thing to know what you struggle with, but it's another thing to actually have opportunties to work on it. Try to find practice with people you're comfortable with. I joined an integrated youth group for people with intellectual disabilities, who I found non-intimidating and at my social level, and that improved my confidence. For yourself, your opportunity for practice might be volunteering or at a mutual interest group. Take time to explore what would work for you, but make sure you have the opportunity to regularly practice.
Hope this helps. 
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Given a “tentative” diagnosis as a child as I needed services at school for what was later correctly discovered to be a major anxiety disorder.
This misdiagnosis caused me significant stress, which lessened upon finding out the truth about myself from my current and past long-term therapists - that I am an anxious and highly sensitive person but do not have an autism spectrum disorder.
My diagnoses - social anxiety disorder and obsessive-compulsive disorder.
I’m no longer involved with the ASD world.