Resources on exterior algebra, wedge product, geometric product and tensors

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I would like to learn exterior algebra, wedge product and geometric product along with their applications in physics. Is there a good source you can recommend? Should I study differential geometry in order to grasp them? I started studying tensor analysis but even the concept of contravariance and covariance is not explained well enough in most of the textbooks. I would be grateful if you point at a source that guides one well and assumes no prior knowledge of the topics except calculus and linear algebra.

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Personally, when I came to the subject of exterior algebra I found no better a text than R.W.R Darling's Differential Forms and Connections: see link here