diff --git a/src/fp.rs b/src/fp.rs
new file mode 100644
index 000000000..c91a9190e
--- /dev/null
+++ b/src/fp.rs
@@ -0,0 +1,5 @@
+//! This module provides an implementation of the BLS12-381 base field `GF(p)`
+//! where `p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab`
+
+#[derive(Copy, Clone, Debug)]
+pub struct Fp;
diff --git a/src/fp2.rs b/src/fp2.rs
new file mode 100644
index 000000000..848fc472c
--- /dev/null
+++ b/src/fp2.rs
@@ -0,0 +1,9 @@
+//! This module implements arithmetic over the quadratic extension field Fp2.
+
+use crate::fp::Fp;
+
+#[derive(Copy, Clone, Debug)]
+pub struct Fp2 {
+    pub c0: Fp,
+    pub c1: Fp,
+}
diff --git a/src/g1.rs b/src/g1.rs
new file mode 100644
index 000000000..607cf2739
--- /dev/null
+++ b/src/g1.rs
@@ -0,0 +1,25 @@
+//! This module provides an implementation of the G1 group of BLS12-381.
+
+use crate::fp::Fp;
+use subtle::Choice;
+
+/// This is an element of G1 represented in the affine (x, y) coordinate space. It
+/// is ideal to keep elements in this representation to reduce memory usage and
+/// improve performance through the use of mixed curve model arithmetic.
+///
+/// Values of `G1Affine` are guaranteed to be in the q-order subgroup unless an
+/// "unchecked" API was misused.
+#[derive(Copy, Clone, Debug)]
+pub struct G1Affine {
+    x: Fp,
+    y: Fp,
+    infinity: Choice,
+}
+
+/// This is an element of G1 represented in the projective (X, Y, Z) coordinate space.
+#[derive(Copy, Clone, Debug)]
+pub struct G1Projective {
+    x: Fp,
+    y: Fp,
+    z: Fp,
+}
diff --git a/src/g2.rs b/src/g2.rs
new file mode 100644
index 000000000..018f54ea3
--- /dev/null
+++ b/src/g2.rs
@@ -0,0 +1,25 @@
+//! This module provides an implementation of the G2 group of BLS12-381.
+
+use crate::fp2::Fp2;
+use subtle::Choice;
+
+/// This is an element of G2 represented in the affine (x, y) coordinate space. It
+/// is ideal to keep elements in this representation to reduce memory usage and
+/// improve performance through the use of mixed curve model arithmetic.
+///
+/// Values of `G2Affine` are guaranteed to be in the q-order subgroup unless an
+/// "unchecked" API was misused.
+#[derive(Copy, Clone, Debug)]
+pub struct G2Affine {
+    x: Fp2,
+    y: Fp2,
+    infinity: Choice,
+}
+
+/// This is an element of G2 represented in the projective (X, Y, Z) coordinate space.
+#[derive(Copy, Clone, Debug)]
+pub struct G2Projective {
+    x: Fp2,
+    y: Fp2,
+    z: Fp2,
+}
diff --git a/src/lib.rs b/src/lib.rs
index e0c6e2a11..d73c8f66a 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -29,3 +29,17 @@ mod util;
 mod scalar;
 
 pub use scalar::Scalar;
+
+#[cfg(feature = "groups")]
+mod fp;
+#[cfg(feature = "groups")]
+mod fp2;
+#[cfg(feature = "groups")]
+mod g1;
+#[cfg(feature = "groups")]
+mod g2;
+
+#[cfg(feature = "groups")]
+pub use g1::{G1Affine, G1Projective};
+#[cfg(feature = "groups")]
+pub use g2::{G2Affine, G2Projective};