diff --git a/src/group.h b/src/group.h
index 2087ee8..cc6cc17 100644
--- a/src/group.h
+++ b/src/group.h
@@ -4,50 +4,100 @@
 #include "num.h"
 #include "field.h"
 
+/** A group element of the secp256k1 curve, in affine coordinates. */
 typedef struct {
     secp256k1_fe_t x;
     secp256k1_fe_t y;
-    int infinity;
+    int infinity; // whether this represents the point at infinity
 } secp256k1_ge_t;
 
+/** A group element of the secp256k1 curve, in jacobian coordinates. */
 typedef struct {
-    secp256k1_fe_t x;
-    secp256k1_fe_t y;
+    secp256k1_fe_t x; // actual X: x/z^2
+    secp256k1_fe_t y; // actual Y: y/z^3
     secp256k1_fe_t z;
-    int infinity;
+    int infinity; // whether this represents the point at infinity
 } secp256k1_gej_t;
 
+/** Global constants related to the group */
 typedef struct {
-    secp256k1_num_t order;
-    secp256k1_ge_t g;
+    secp256k1_num_t order; // the order of the curve (= order of its generator)
+    secp256k1_ge_t g; // the generator point
+
+    // constants related to secp256k1's efficiently computable endomorphism
     secp256k1_fe_t beta;
     secp256k1_num_t lambda, a1b2, b1, a2;
 } secp256k1_ge_consts_t;
 
 static secp256k1_ge_consts_t *secp256k1_ge_consts = NULL;
 
+/** Initialize the group module. */
 void static secp256k1_ge_start(void);
+
+/** De-initialize the group module. */
 void static secp256k1_ge_stop(void);
+
+/** Set a group element equal to the point at infinity */
 void static secp256k1_ge_set_infinity(secp256k1_ge_t *r);
+
+/** Set a group element equal to the point with given X and Y coordinates */
 void static secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y);
+
+/** Check whether a group element is the point at infinity. */
 int  static secp256k1_ge_is_infinity(const secp256k1_ge_t *a);
+
 void static secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a);
+
+/** Get a hex representation of a point. *rlen will be overwritten with the real length. */
 void static secp256k1_ge_get_hex(char *r, int *rlen, const secp256k1_ge_t *a);
+
+/** Set a group element equal to another which is given in jacobian coordinates */
 void static secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a);
 
+
+/** Set a group element (jacobian) equal to the point at infinity. */
 void static secp256k1_gej_set_infinity(secp256k1_gej_t *r);
+
+/** Set a group element (jacobian) equal to the point with given X and Y coordinates. */
 void static secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y);
+
+/** Set a group element (jacobian) equal to the point with given X coordinate, and given oddness for Y.
+    The result is not guaranteed to be valid. */
 void static secp256k1_gej_set_xo(secp256k1_gej_t *r, const secp256k1_fe_t *x, int odd);
+
+/** Set a group element (jacobian) equal to another which is given in affine coordinates. */
 void static secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a);
+
+/** Get the X coordinate of a group element (jacobian). */
 void static secp256k1_gej_get_x(secp256k1_fe_t *r, const secp256k1_gej_t *a);
+
+/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
 void static secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a);
+
+/** Check whether a group element is the point at infinity. */
 int  static secp256k1_gej_is_infinity(const secp256k1_gej_t *a);
+
+/** Check whether a group element (jacobian) is valid (i.e., on the curve). */
 int  static secp256k1_gej_is_valid(const secp256k1_gej_t *a);
+
+/** Set r equal to the double of a. */
 void static secp256k1_gej_double(secp256k1_gej_t *r, const secp256k1_gej_t *a);
+
+/** Set r equal to the sum of a and b. */
 void static secp256k1_gej_add(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b);
+
+/** Set r equal to the sum of a and b (with b given in jacobian coordinates). This is more efficient
+    than secp256k1_gej_add. */
 void static secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b);
+
+/** Get a hex representation of a point. *rlen will be overwritten with the real length. */
 void static secp256k1_gej_get_hex(char *r, int *rlen, const secp256k1_gej_t *a);
+
+/** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */
 void static secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a);
+
+/** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (given that a is
+    not more than 256 bits). */
 void static secp256k1_gej_split_exp(secp256k1_num_t *r1, secp256k1_num_t *r2, const secp256k1_num_t *a);
 
 #endif