These pdfs introduce the young or old beginning learner ( but serious! ) with the very basics of the algebra and calculus for grasping GR ( General Relativity ), namely:

1). a very, very brief vector and tensor analysis;

2). the orthonormal ( at right angles to each other ) curvilinear basis vectors;

3). the foundational so-called "metric tensor" g where the 'g' represents the intensity of the gravity field throughout a varying position in space;

4). finally, the famous "Riemann Flat Spacetime Metric" which is analogous to flat Euclidean space but more generalized to include time as a 4th axis to the geometry of analysis.

The calculus itself is basic. Nevertheless the learner is guided step-by-step thru the mechanics of the calculus involved. It will, further, encourage the serious young or old learner to get to another book to, say, look around the calculus at the same time learning this particular subject of GR.

Still, good luck! Go slow yet learn one of the most formidable aspects of 20th century physics!