diff --git a/include/kkt.h b/include/kkt.h
new file mode 100644
index 0000000..9560d5e
--- /dev/null
+++ b/include/kkt.h
@@ -0,0 +1,109 @@
+#ifndef KKT_H
+# define KKT_H
+
+# ifdef __cplusplus
+extern "C" {
+# endif // ifdef __cplusplus
+
+# include "types.h"
+
+# ifndef EMBEDDED
+
+#  include "cs.h"
+
+/**
+ * Form square symmetric KKT matrix of the form
+ *
+ * [P + param1 I,            A';
+ *  A             -diag(param2)]
+ *
+ * NB: Only the upper triangular part is stuffed!
+ *
+ *
+ *  If Pdiag_idx is not OSQP_NULL, it saves the index of the diagonal
+ * elements of P there and the number of diagonal elements in Pdiag_n.
+ *
+ * Similarly, if rhotoKKT is not null,
+ * it saves where the values of param2 go in the final KKT matrix
+ *
+ * NB: Pdiag_idx needs to be freed!
+ *
+ * @param  P          cost matrix (already just upper triangular part)
+ * @param  A          linear constraint matrix
+ * @param  format     CSC (0) or CSR (1)
+ * @param  param1     regularization parameter
+ * @param  param2     regularization parameter (vector)
+ * @param  PtoKKT     (modified) index mapping from elements of P to KKT matrix
+ * @param  AtoKKT     (modified) index mapping from elements of A to KKT matrix
+ * @param  Pdiag_idx  (modified) Address of the index of diagonal elements in P
+ * @param  Pdiag_n    (modified) Address to the number of diagonal elements in P
+ * @param  param2toKKT    (modified) index mapping from param2 to elements of
+ *KKT
+ * @return            return status flag
+ */
+csc* form_KKT(const csc  *P,
+              const  csc *A,
+              c_int       format,
+              c_float     param1,
+              c_float    *param2,
+              c_int      *PtoKKT,
+              c_int      *AtoKKT,
+              c_int     **Pdiag_idx,
+              c_int      *Pdiag_n,
+              c_int      *param2toKKT);
+# endif // ifndef EMBEDDED
+
+
+# if EMBEDDED != 1
+
+/**
+ * Update KKT matrix using the elements of P
+ *
+ * @param KKT       KKT matrix in CSC form (upper-triangular)
+ * @param P         P matrix in CSC form (upper-triangular)
+ * @param PtoKKT    Vector of pointers from P->x to KKT->x
+ * @param param1    Parameter added to the diagonal elements of P
+ * @param Pdiag_idx Index of diagonal elements in P->x
+ * @param Pdiag_n   Number of diagonal elements of P
+ */
+void update_KKT_P(csc          *KKT,
+                  const csc    *P,
+                  const c_int  *PtoKKT,
+                  const c_float param1,
+                  const c_int  *Pdiag_idx,
+                  const c_int   Pdiag_n);
+
+
+/**
+ * Update KKT matrix using the elements of A
+ *
+ * @param KKT       KKT matrix in CSC form (upper-triangular)
+ * @param A         A matrix in CSC form (upper-triangular)
+ * @param AtoKKT    Vector of pointers from A->x to KKT->x
+ */
+void update_KKT_A(csc         *KKT,
+                  const csc   *A,
+                  const c_int *AtoKKT);
+
+
+/**
+ * Update KKT matrix with new param2
+ *
+ * @param KKT           KKT matrix
+ * @param param2        Parameter of the KKT matrix (vector)
+ * @param param2toKKT   index where param2 enters in the KKT matrix
+ * @param m             number of constraints
+ */
+void update_KKT_param2(csc           *KKT,
+                       const c_float *param2,
+                       const c_int   *param2toKKT,
+                       const c_int    m);
+
+# endif // EMBEDDED != 1
+
+
+# ifdef __cplusplus
+}
+# endif // ifdef __cplusplus
+
+#endif // ifndef KKT_H