I agree with Johannes's comment, but despite this, one book that might fit your criteria is Theory of distributions by M.A. Al-Gwaiz. I haven't looked at it for some months, but it made the following standard texts more accessible:

• Friedlander and M. Joshi's Introduction to the Theory of Distributions.
• Hörmander's The Analysis of Linear Partial Differential Operators.

A book that I haven't looked at thoroughly, but you might find interesting, is Guide to Distribution theory and Fourier transforms by Robert S. Strichartz. I once took a class with the author, whose verbal explanatory style is complete and who is also a clear writer.

I agree with Johannes's comment, but despite this, one book that might fit your criteria is Theory of distributions by M.A. Al-Gwaiz. I haven't looked at it for some months, but made the following standard texts more accessible:

• Friedlander and M. Joshi's Introduction to the Theory of Distributions.
• Hörmander's The Analysis of Linear Partial Differential Operators.

A book that I haven't looked thoroughly, but you might find interesting is Guide to Distribution theory and Fourier transforms by Robert S. Strichartz. I once took a class with the author, whose verbal explanatory style is complete and who is also a clear writer.