Many who have lightly dabbled with quantum mechanics are aware of how electrons aren't really particles, they're waves with ill-defined positions and velocities. But what does this really mean? Much of the way we think about physics has changed drastically since the start of the 20th century, particularly due to the contributions of Einstein's relativity and quantum mechanics. This course uses calculus and some linear algebra to introduce the basic ideas behind quantum mechanics and begin to work through both the mathematical and philosophical underpinnings of this strange, non-intuitive branch of physics.