Framework for implementing and maintaining a QMS

Is there any framework or theory that can be recommended for implementing and maintaining a QMS related to quality certifications? What I am searching for is the organizational content of getting certified, because for my study I need to write a thesis which relates to the Quality department of an organization.

Yes, Advisera suggests a framework for implementing and maintaining a QMS in order to get and keep certification. Bellow, you can find some articles about our framework based on years of experience.

And do you consult companies on organizing or structuring their ''Quality'' department? If so, do you use theory to do that, and which theory is that?

Based on our experience we designed a course about implementing a QMS and an Implementation Toolkit to speed up implementation. Bellow, you can find a link to such Lead Implementer Course and Documentation Toolkit.

Please note that Advisera's materials are fully aligned with ISO 9001 and IATF 16949. The following material will provi de you with information about implementing a QMS:
- Checklist of ISO 9001 implementation & certification steps
https://advisera.com/9001academy/knowledgebase/checklist-of-iso-9001-implementation-certification-steps/
- What are the biggest challenges while setting up an ISO 9001-based QMS, and how do you overcome them?
https://advisera.com/9001academy/blog/2016/06/28/what-are-the-biggest-challenges-while-setting-up-an-iso-9001-based-qms-and-how-do-you-overcome-them/
- ISO 9001 Implementation diagram
https://info.advisera.com/9001academy/free-download/iso-9001-implementation-diagram
- ISO 9001:2015 Documentation Toolkit
https://advisera.com/9001academy/iso-9001-documentation-toolkit/
- You can enroll for free in this ISO 9001:2015 Lead Implementer Course
https://advisera.com/training/iso-9001-lead-implementer-course/
- ISO 9001:2015 Foundations Course
https://advisera.com/training/iso-9001-foundations-course/
- book - Discover ISO 9001:2015 Through Practical Examples
https://advisera.com/books/discover-iso-9001-2015-through-practical-examples/