If you're getting started in the data science world, here's a few libraries that you need to check out. The important thing with 'learning' a library is to find a reason to use it. You need a real project to make it stick!
Starting with the sexy stuff up front, this is what I use to ship real production machine learning. This covers about 80% of what I do, the rest is largely logistical (and cloud engineering!)
scikit-learn - Duh. It's used everywhere because it's really good. Check out the tutorials, find some data, and fit some lines!
River - This library is badass if you need updatable (streaming!) models. I use thousands of their regressions models to project the output of thousands of devices, every day at work. The bottleneck is the database! Plays nicely with pickle too.
Scipy stands alone because it is incredibly useful for feature engineering, but has kickass data structures too. Have sparse data?
scipy.sparse is your new best friend. I used it to run ML on a multi-million column matrix with no issues. Lots of help with linear algebra, preprocessing, and signal processing (which will be a whole article some day). Also some statistical programming help that scikit-learn lacks.
find_peaks is my latest obsession, it's just really good.
Data Structures and Manipulation
numpy - Kind of a pain to work with, but really good at what it does. If it needs to be fast, it needs to be numpy. Multidimensional arrays, matrix math, and data cleaning can be done with numpy. It is hard to learn on its own, but 101 Numpy Exercises will get you there.
pandas - Slower than numpy for most things, but not slower by dev time. If you're dealing with time series data, go this route. Handles datetimes exceptionally well. Very useful for reading/writing csv's, as the Python builtin is clunky. Can pull directly from sql/csv's/parquet too. Rolling statistics are a particular joy, rolling median is remarkably hard to implement in numpy. All? I believe? of scikit-learn supports pandas' DataFrames as inputs, so go this route if you're starting out.
smart-open - Replaces open. Provides s3 (and WAY more) support. Stupidly useful. Reading in a csv from s3? Use this with pandas.
For regular Python data (in lists, dictionaries, etc):
collections - Counter is super useful, and FAST.
itertools - Different ways to iterate or combine data. Product, groupby, and chain are very useful.
matplotlib - It isn't always pretty, and it is always easy, but if it's a quick graph for myself, it's in matplotlib. Plays very nicely in notebooks, less useful in production.
plotly - Interactive charts, handy as hell, can be iteratively generated too. Can be saved off as standalone html files, which I send to my experts for feedback when we're building a model!
Get to work!
That is most of what you need to do the daily work of a data scientist. Sometimes you'll find a specific problem (especially in signal processing!) that might have a better specialty package. Search Medium and Google for those! Kalman filters are a great example, good luck writing one yourself without