Is it permissible? Do I need to specifically mention it somewhere in my thesis?
The Apache license allows use for any purpose, so using the code in a thesis is fine.
However, it is common to cite relevant libraries and software that you used in an academic context. This is entirely an academic thing and has nothing to do with licenses.
You can cite the project website or the code repository website as you would cite any other website. Sometimes, software that originated from academia also has "how to cite" instructions, e.g. when the authors wrote a paper that presented the software. For example, the SciPy software that is often used in Python has such information here.
: don't cite everything that you used, but cite software that is relevant in the context of the thesis. E.g. when researching optimization algorithms, don't cite your version control system, your operating system, or that you are using LaTeX. In contrast, do cite other optimization tools that you used or inspired you, and other libraries that were essential in doing your project.
The Apache License v2.0 states that you have a "perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable copyright license to reproduce, prepare Derivative Works of, publicly display, publicly perform, sublicense, and distribute" the software, so you can freely reproduce the source code in your thesis.
However, an orthogonal concept to copyright is plagiarism. To avoid plagiarism, you must, at the minimum, clearly cite the source of the reproduced source code. Plagiarism is unrelated to copyright and is not a law (in any country I've heard of) but is almost certainly a policy at your university and is considered unethical.