What are the types of ab initio Molecular Dynamics?

I am new to the world of Molecular Dynamics, and am curious to know exactly what is considered to be an ab initio Molecular Dynamics (AIMD) method, and how do they work?

The seminal work by Roberto Car and Michele Parrinello, titled "Unified Approach for Molecular Dynamics and Density-Functional Theory" was published 35 years ago!

I have recently come across the following "types" of MD methods while reading some research papers:

• Born-Oppenheimer Molecular Dynamics
• Car-Parinello Molecular Dynamics [link to answer]
• 2nd generation CPMD
• Approximate Car-Parrinello-like Langevin Born-Oppenheimer Molecular Dynamics
• Many-body Molecular Dynamics
• ab initio Ehrenfest Dynamics
• TDDFT/MD

If I am missing methods, which I am sure I am, please feel free to add them through an answer!Also, it would be appreciated if one method is explained per answer, and is summarized in 2-3 paragraphs.