Your resume should be tailored for the job that you are applying for. If you have skills that you have developed that are related or transferrable to your resume, by all means add it.
Your Linkedin profile should resonate with your resume. The fact that you are a self-directed learner would fit in well with your profile. If there is some sort of a diploma or certificate that you have earned add it to your Experience section of your Linkedin profile.
I don’t think mentioning that you have read books on specific topics will give you much impact but it might be a good idea to drop it into conversation when you are being interviewed. Then, provide an example of what you have learned.
As originally answered on Quora.com