All the libraries are open source and you can find them in PyPI. Based on the requirement, reviews and user-based, here is the list.
1. Matplotlib: Used for data analysis and numerical plotting in Python.
2. Pandas: Used for analysing data, and reading the data in Python.
3. NumPy: Used for working with arrays in Python.
4. SciPy: Used for optimization, stats and signal to the process in Python.
5. TensorFlow: Used for high-level computations in Python.
6. Scikit-learn: Used for working with complex data in Python.
7. PyGame: Used for developing video games in Python.
8. PyTorch: Used for optimizing tensor computations in Python.
9. PyBrain: Used for machine learning tasks in Python.
10. Django: Used for Web Development in Python
11. Flask: Used for Web Development, and specifically for API development in Python.
12. Keras: Used for building neural network blocks in Python.
13. LightGBM: Used for building new algorithms in Python.
14. Eli5: Used for Legacy applications and implementing newer methodologies in various fields of python.
15. Theano: Used for computing multidimensional arrays in Python.
16. Math Function: This module provides access to the mathematical functions defined by the C standard in Python.
17. SymPy: Used for symbolic Math and is a full-fledged CAS in Python.
18. PyGTK: Used for creating programs with a Graphical User Interface with Python.
19. Beautiful Soup: Used for pulling data out of HTML and XML files in Python.
20. Pytz: Used for time-zone calculations in our Python applications in Python
21. requests: Used for making HTTP requests to a specified URL.
22. Pytest: Used for writting API test cases.
23. DataNitro: used for integrating Excel with Python.
24. FlashText: Used for replacing keywords in sentences or extracting keywords from sentences
25. OpenCV: Used for computer vision, machine learning, and image processing.
26. NLTK: Used for building Python programs to work with human language data.
27. Fire: Used for creating CLI applications.
28. Arrow: Used for working with date and time
29. SQLAlchemy: Used for working with the language’s own objects, and not writing separate SQL queries.
30. wxPython: Used for creating a highly functional graphical user interface.
31. Cirq: Used For for writing, manipulating, and optimizing quantum circuits and running them against quantum computers and simulators.
32. Luminoth: Used for object detection.
33. Delorean: Used for clearing up the inconvenient truths that arise dealing with datetimes in Python.
34. Bokeh: Used for rendering plots using HTML and JavaScript that uses modern web browsers for presenting elegant, concise construction of novel graphics with high-level interactivity.
35. Poetry: Used for dependency management and packaging in Python.
36. Gensim: Used for topic modelling, document indexing and similarity retrieval with large corpora.
37. yfinanceapi: an API for Python that builds on top of the Yahoo! finance JSON API to provide equity and currency information, such as price, volume, last trade time etc.
38. Networkx: Used for the creation, manipulation, and study of the structure, dynamics, and function of complex networks.
39. TextBlob: used for processing textual data.
40. empirical: provides a way to model and sample cumulative probabilities for a data sample that does not fit a standard probability distribution.
41. Spark MLlib: Used for Bigdata Machine learning.
42. StatsModels: provides a complement to scipy for statistical computations including descriptive statistics and estimation and inference for statistical models.
43. Seaborn: provides a high-level interface for drawing attractive and informative statistical graphics.
44. Plotly: used for data visualization and understanding data simply and easily.
45. XGBoost: stands for Extreme Gradient Boosting, which was proposed by the researchers at the University of Washington.
46. Selenium: Selenium is a powerful tool for controlling web browsers through programs and performing browser automation
47. Scrapy: used for extracting the data you need from websites.
48. PyGObject: Provides bindings for GObject-based libraries such as GTK, GStreamer, WebKitGTK, GLib, GIO and many more.
49. PYGLET: Used for object-oriented application programming interface for the creation of games and other multimedia applications.
50. CuPy: It is a NumPy/SciPy-compatible array library for GPU-accelerated computing with Python.
51. pyfolio: for performance and risk analysis of financial portfolios developed by Quantopian Inc.
52. QuTip: Used for the Quantum Toolbox in Python
53. RDFLib: RDFLib is a Python library for working with RDF
54. spaCy: Used to build real products, or gather real insights.
55. quantdsl: is a functional programming language for modelling derivative instruments.
56. PyQt: It is a Graphical User Interface widgets toolkit
57. ffn: It is a library that contains many useful functions for those who work in quantitative finance.
58. pysabr: It is a Financial plugin.
59. pandas_talib: It is A Python Pandas implementation of technical indicators
60. pyalgotrade: is a Python Algorithmic Trading Library with focus on backtesting and support for paper-trading and live-trading.
61. zipline: It is a Pythonic algorithmic trading library.
62. QuantSoftware Toolkit: Used to support portfolio construction and management.
63. bt: used to test quantitative trading strategies.