Newton's First Law

Newton's first law states that when net force is 0, objects at rest stay at rest, and objects that are not at rest will move at constant velocity. Note that a net force of 0 doesn't necessarily imply no forces are being applied. For example, if one puts a book on a table. The book stays at rest because the normal force of the table and the gravitational pull of the Earth cancel each other out, creating a net force of 0. Another application of Newton's first law is the concept of terminal velocity. When something is dropped within Earth's atmosphere, at first the net force isn't 0 due to gravity, so the thing starts to accelerate. However, as it gains velocity, drag force also increases. There will eventually be a point when the drag force become equal to gravity. At that point, the net force on the object is 0, and thus it'll move at constant velocity.

Every body continues in its state of rest or uniform motion unless an external force is impressed upon it.

Newton's First Law: An object at rest stays at rest and an object in motion remains in motion unless acted upon by an external force

This is also known as the law of inertia.

This means that when you throw a ball in space, the ball will almost surely continue indefinitely because, in the vacuum of space, there is probably nothing to stop it.

Instead of just writing down what Newton's First Law is like everyone else, let us think deeper.

Newton's Second Law tells us that $$F = \frac{\mathrm{d}p}{\mathrm{d}t}$$

so that when the change in momentum is $0$, the resultant force is zero and it is thus obvious that an object will move at constant velocity or remain at rest.

This is essentially Newton's First Law, so does this not mean that Newton's First Law is a specific case of Newton's Second Law for zero net force? What is the difference between Newton's First Law and Newton's Second Law?

Well, Newton's First Law defines clearly for us what an inertial frame of reference is and that is its purpose. An inertial frame of reference is simply a non-accelerating frame of reference. For accelerating frames of reference, it becomes more complicated and fictitious forces will come into play.