The essential mathematics underlying special relativity
is a
- mild generalization of Euclidean Geometry (called Minkowski spacetime geometry)
- mild generalization of circular trigonometry
(called hyperbolic trigonometry [not to be confused with hyperbolic geometry])
- mild generalization of vector algebra in Euclidean space (using the Minkowski dot-product).

Learn relativity from a modern relativist,
who thinks first in terms of constructions on position-vs-time graphs (a.k.a. spacetime diagrams),
rather than "effects" and Lorentz transformation formulas.
(You don't learn high-school geometry by studying rotation matrices.
You learn by drawing geometric figures then understanding relationships among them,
like scaling, intersections, parallelism, and tangency [related to perpendicularity].)

Advice:
Quickly learn to translate between the physics,
the "words in a problem", the geometry in a spacetime diagram,
and the associated vectorial expressions.

Advice:
Try to appreciate "operational definitions" of things,
e.g. "radar methods" involving light-signals and light-cones.
Appreciate Minkowski's characterization of "normal" or "perpendicular":
"the tangent-line to a circle is perpendicular to the radius".

Advice:
work in natural units so that c = (3e8 m/s) doesn't show up in calculations.
Use seconds and light-seconds, not seconds and meters.
Use arithmetically convenient values like v=(3/5)c and v=(4/5)c
[in the beginning, avoid v=(1/2)c, v=(0.99)c, v=(0.999)c..
because these lead to unnecessary and distracting arithmetic,
obscuring geometric and physical understanding].

Use the geometry (not just words or formulas)
to scaffold your understanding and intuition of the physics.

Many introductory problems in special relativity
are essentially hyperbolic-trigonometric analogues
of problems involving solving for some unknown feature in a right-triangle,
which arise by drawing a spacetime diagram of the situation.

Avoid:
- approaches involving Loedel diagrams and Epstein diagrams
(and any other attempt to use Euclidean geometry because they claim
that Minkowski spacetime geometry is too hard)
- asking about the frame of a light-signal (there is no such frame)
- the phrase that "we are all traveling through spacetime at the speed of light" (it sounds profound, but it's making a mountain out of a molehill... and is not useful to be elevating the notion of a "unit vector")
- thinking only in terms of "space" ... using moving boxcars.