diff --git a/.gitignore b/.gitignore
index b0ac550..65d0183 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,4 +1,5 @@
 *.o
-SM-MaponiA3
-Sherman-Morrison
+*.mod
+cppSherman-Morrison
+fSherman-Morrison
 .vscode
\ No newline at end of file
diff --git a/Makefile b/Makefile
index 24460e3..b7182d2 100644
--- a/Makefile
+++ b/Makefile
@@ -1,17 +1,30 @@
-CC=icc
 CXX=icpc
-CFLAGS=-O0 -debug full
 CXXFLAGS=-O0 -debug full -traceback
+FC=ifort
+FFLAGS=-O0 -debug full -traceback
 # ARCH=-xCORE-AVX2 
 
-DEPS = SM-MaponiA3.cpp
-OBJ = SM-MaponiA3.o main.o
+## Deps & objs for the C++ stuff
+cppDEPS = cppmain.cpp SM_MaponiA3.cpp SM_MaponiA3.hpp Helpers.hpp
+cppOBJ = cppmain.o SM_MaponiA3.o
+## Deps & objs for the Fortran stuff
+fDEPS = fmain.f90 SM_MaponiA3_mod.f90
+fOBJ = SM_MaponiA3_mod.o fmain.o
 
-%.o: %.cpp $(DEPS)
-	$(CXX) $(ARCH) -c -o $@ $< $(CFLAGS)
+%.o: %.cpp $(cppDEPS)
+	$(CXX) $(ARCH) $(CXXFLAGS) -c -o $@ $<
 
-Sherman-Morrison: $(OBJ)
-	$(CXX) $(ARCH) -o $@ $^ $(CFLAGS)
+%.o: %.f90 $(fDEPS)
+	$(FC) $(ARCH) $(FFLAGS) -c -o $@ $<
+
+all: cppSherman-Morrison fSherman-Morrison
+
+cppSherman-Morrison: $(cppOBJ)
+	$(CXX) $(ARCH) $(CXXFLAGS) -o $@ $^
+
+fSherman-Morrison: $(fOBJ)
+	$(FC) $(ARCH) $(FFLAGS) -o $@ $^
 
 clean:
-	@rm -vf *.o
+	@rm -vf *.o *.mod
+	
\ No newline at end of file
diff --git a/SM-MaponiA3.hpp b/SM-MaponiA3.hpp
deleted file mode 100644
index 9b5a48f..0000000
--- a/SM-MaponiA3.hpp
+++ /dev/null
@@ -1,3 +0,0 @@
-// SM-MaponiA3.hpp
-
-void Sherman_Morrison(int **Slater0, double **Slater_inv, unsigned int *Dim, unsigned int *N_updates, int **Updates, unsigned int *Updates_index);
\ No newline at end of file
diff --git a/SM-MaponiA3.cpp b/SM_MaponiA3.cpp
similarity index 94%
rename from SM-MaponiA3.cpp
rename to SM_MaponiA3.cpp
index df94ef2..a652fe2 100644
--- a/SM-MaponiA3.cpp
+++ b/SM_MaponiA3.cpp
@@ -1,10 +1,10 @@
 // SM-MaponiA3.cpp
 // Algorithm 3 from P. Maponi,
 // p. 283, doi:10.1016/j.laa.2006.07.007
-#include "SM-MaponiA3.hpp"
+#include "SM_MaponiA3.hpp"
 #include "Helpers.hpp"
 
-void Sherman_Morrison(int **Slater0, double **Slater_inv, unsigned int *Dim, unsigned int *N_updates, int **Updates, unsigned int *Updates_index) {
+void Sherman_Morrison_(int **Slater0, double **Slater_inv, unsigned int *Dim, unsigned int *N_updates, int **Updates, unsigned int *Updates_index) {
     unsigned int k, l, lbar, i, j, tmp, M = *Dim;
     unsigned int *p = new unsigned int[M+1];
     unsigned int **Id = new unsigned int*[M];
diff --git a/SM_MaponiA3.hpp b/SM_MaponiA3.hpp
new file mode 100644
index 0000000..065d662
--- /dev/null
+++ b/SM_MaponiA3.hpp
@@ -0,0 +1,5 @@
+// SM-MaponiA3.hpp
+
+extern "C" {
+    void Sherman_Morrison_(int **Slater0, double **Slater_inv, unsigned int *Dim, unsigned int *N_updates, int **Updates, unsigned int *Updates_index);    
+}
\ No newline at end of file
diff --git a/SM_MaponiA3_mod.f90 b/SM_MaponiA3_mod.f90
new file mode 100644
index 0000000..c1d9e91
--- /dev/null
+++ b/SM_MaponiA3_mod.f90
@@ -0,0 +1,11 @@
+module MYMODULE
+    interface
+        subroutine MYSUBROUTINE(Slater0, Slater_inv, dim, n_updates, Updates, Updates_index) bind(C, name="Sherman_Morrison")
+            use, intrinsic :: iso_c_binding, only : c_int, c_double
+            integer(c_int), intent(in) :: dim, n_updates
+            integer(c_int), dimension(:), allocatable, intent(in) :: Updates_index
+            integer(c_int), dimension(:,:), allocatable, intent(in) :: Slater0, Updates
+            real(c_double), dimension(:,:), allocatable, intent(in out) :: Slater_inv
+        end subroutine MYSUBROUTINE
+    end interface
+end module MYMODULE
\ No newline at end of file
diff --git a/main.cpp b/cppmain.cpp
similarity index 96%
rename from main.cpp
rename to cppmain.cpp
index 55af456..79671a5 100644
--- a/main.cpp
+++ b/cppmain.cpp
@@ -1,5 +1,5 @@
 // main.cpp
-#include "SM-MaponiA3.hpp"
+#include "SM_MaponiA3.hpp"
 #include "Helpers.hpp"
 #include <cstdlib>
 #include <ctime>
@@ -65,7 +65,7 @@ int main() {
     // Define pointers dim and n_updates to use in Sherman-Morrison(...) function call
     unsigned int *dim = new unsigned int(M);
     unsigned int *n_updates = new unsigned int(M);
-    Sherman_Morrison(A0, A0_inv, dim, n_updates, Ar, Ar_index);
+    Sherman_Morrison_(A0, A0_inv, dim, n_updates, Ar, Ar_index);
     showMatrix(A0_inv, M, "A0_inv");
     
     // Deallocate all vectors and matrices 
diff --git a/fmain.f90 b/fmain.f90
new file mode 100644
index 0000000..44a2a53
--- /dev/null
+++ b/fmain.f90
@@ -0,0 +1,35 @@
+program Interface_test
+    use, intrinsic :: iso_c_binding, only : c_int, c_double
+    use MYMODULE, only : MYSUBROUTINE
+    implicit none
+
+    integer i, j !! Iterators
+    integer(c_int) :: dim, N_updates
+    integer(c_int), dimension(:), allocatable :: Ar_index
+    integer(c_int), dimension(:,:), allocatable :: A, A0, Ar
+    real(c_double), dimension(:,:), allocatable :: A0_inv
+
+    dim = 3
+    N_updates = dim
+    allocate(Ar_index(dim), A(dim,dim), A0(dim,dim), Ar(dim,dim), A0_inv(dim,dim))
+
+    !! Initialize A with M=3 and fill acc. to Eq. (17) from paper
+    A(1,1) = 1
+    A(1,2) = 1
+    A(1,3) = -1
+    A(2,1) = 1
+    A(2,2) = 1
+    A(2,3) = 0
+    A(3,1) = -1
+    A(3,2) = 0
+    A(3,3) = -1
+
+    do i=1,3
+        do j=1,3
+            write(*,"(I)", advance="no") A(i,j)
+        end do
+        write(*,*)
+    end do
+
+    deallocate(Ar_index, A, A0, Ar, A0_inv)
+end program