The Stanford d.school is one of the birth places of Design Thinking and one of the most renowned places where you can learn the technics and skills. The school believes that everyone has the capacity to be creative. The Stanford d.school wants therefore to be a place where people use design to develop their own creative potential. Their Design Thinking Process is maybe one of the most well know Design process out there and has been used as a basis for many other processes.
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Strangely enough one of the things that I particularly like about this process is one of the tiniest thing in there. It's the "*" sign. When you follow this sign it brings you to a footnote which says: "not necessarily linear, apply as needed". When my mate Pascal Wicht explains this process he often uses the metaphor of the toolbox. Each part of the process is like a tool in a toolbox. You just pick the tool that will help you with the problem you are facing. I think this is a particularly strong idea of this process! You can do it in a linear way, but it is definitely okay to use a part of the process when you feel it helps.
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The second thing I particularly like about this process is that in a way it's the basis for most other design and service design processes out there. If you understand this one well, you might have a good understanding of many other design processes. So it's a good investment of your time to learn more about this one as the learnings you make here can be applied to nearly all other processes.

I found the illustration of the process shown here in an article called "Design Thinking models. Stanford d.school" written by Ramunas Balcaitis

The d.school has created tons of ressources to learn Design Thinking on their website. One ressource that you might be especially interested in is the PDF "An Introduction to Design Thinking PROCESS GUIDE" which explains in depth the different building blocks of the Design Thinking process.