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diff --git a/src/Toplex_map/example/simple_toplex_map.cpp b/src/Toplex_map/example/simple_toplex_map.cpp
new file mode 100644
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+++ b/src/Toplex_map/example/simple_toplex_map.cpp
@@ -0,0 +1,153 @@
+/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+ *    Author(s):       Vincent Rouvreau
+ *
+ *    Copyright (C) 2018
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#include <gudhi/Toplex_map.h>
+
+#include <iostream>
+#include <utility>  // for pair
+#include <vector>
+#include <cassert>
+
+int main(int argc, char* const argv[]) {
+  using Simplex = Gudhi::Toplex_map::Simplex;
+  Simplex sigma1 = {1, 2, 3};
+  Simplex sigma2 = {2, 3, 4, 5};
+
+  Gudhi::Toplex_map tm;
+  tm.insert_simplex(sigma1);
+  tm.insert_simplex(sigma2);
+
+  /* Simplex is:   */
+  /*    2   4      */
+  /*    o---o      */
+  /*   /X\5/       */
+  /*  o---o        */
+  /*  1   3        */
+
+  std::cout << "num max simplices = " << tm.num_maximal_simplices() << " - num vertices = " << tm.num_vertices()
+            << std::endl;
+
+  // Browse maximal cofaces
+  Simplex sigma3 = {2, 3};
+  std::cout << "Maximal cofaces of {2, 3} are :" << std::endl;
+  for (auto simplex_ptr : tm.maximal_cofaces(sigma3, 2)) {
+    for (auto v : *simplex_ptr) {
+      std::cout << v << ", ";
+    }
+    std::cout << std::endl;
+  }
+
+  // Browse maximal simplices
+  std::cout << "Maximal simplices are :" << std::endl;
+  for (auto simplex_ptr : tm.maximal_simplices()) {
+    for (auto v : *simplex_ptr) {
+      std::cout << v << ", ";
+    }
+    std::cout << std::endl;
+  }
+
+  Simplex sigma4 = {1, 3};
+  assert(tm.membership(sigma4));
+
+  Gudhi::Toplex_map::Vertex v = tm.contraction(1, 3);
+  std::cout << "After contraction(1, 3) - " << v << std::endl;
+  /* Simplex is:   */
+  /*    2   4      */
+  /*    o---o      */
+  /*     \5/       */
+  /*      o        */
+  /*      3        */
+  std::cout << "num max simplices = " << tm.num_maximal_simplices() << " - num vertices = " << tm.num_vertices()
+            << std::endl;
+
+  // Browse maximal simplices
+  std::cout << "Maximal simplices are :" << std::endl;
+  for (auto simplex_ptr : tm.maximal_simplices()) {
+    for (auto v : *simplex_ptr) {
+      std::cout << v << ", ";
+    }
+    std::cout << std::endl;
+  }
+
+  Simplex sigma5 = {3, 4};
+  assert(tm.membership(sigma5));
+
+  v = tm.contraction(3, 4);
+  std::cout << "After contraction(3, 4) - " << v << std::endl;
+  /* Simplex is:   */
+  /*    2   4      */
+  /*    o---o      */
+  /*     \X/       */
+  /*      o        */
+  /*      5        */
+  std::cout << "num max simplices = " << tm.num_maximal_simplices() << " - num vertices = " << tm.num_vertices()
+            << std::endl;
+
+  // Browse maximal simplices
+  std::cout << "Maximal simplices are :" << std::endl;
+  for (auto simplex_ptr : tm.maximal_simplices()) {
+    for (auto v : *simplex_ptr) {
+      std::cout << v << ", ";
+    }
+    std::cout << std::endl;
+  }
+
+  tm.insert_simplex(sigma1);
+  tm.insert_simplex(sigma2);
+  /* Simplex is:   */
+  /*    2   4      */
+  /*    o---o      */
+  /*   /X\5/       */
+  /*  o---o        */
+  /*  1   3        */
+  tm.remove_simplex(sigma1);
+
+  std::cout << "After remove_simplex(1, 2, 3)" << std::endl;
+  /* Simplex is:   */
+  /*    2   4      */
+  /*    o---o      */
+  /*   / \5/       */
+  /*  o---o        */
+  /*  1   3        */
+  std::cout << "num max simplices = " << tm.num_maximal_simplices() << " - num vertices = " << tm.num_vertices()
+            << std::endl;
+
+  // Browse maximal simplices
+  std::cout << "Maximal simplices are :" << std::endl;
+  for (auto simplex_ptr : tm.maximal_simplices()) {
+    for (auto v : *simplex_ptr) {
+      std::cout << v << ", ";
+    }
+    std::cout << std::endl;
+  }
+
+  tm.remove_vertex(1);
+
+  std::cout << "After remove_vertex(1)" << std::endl;
+  /* Simplex is:   */
+  /*    2   4      */
+  /*    o---o      */
+  /*     \5/       */
+  /*      o        */
+  /*      3        */
+  std::cout << "num max simplices = " << tm.num_maximal_simplices() << " - num vertices = " << tm.num_vertices()
+            << std::endl;
+
+  // Browse maximal simplices
+  std::cout << "Maximal simplices are :" << std::endl;
+  for (auto simplex_ptr : tm.maximal_simplices()) {
+    for (auto v : *simplex_ptr) {
+      std::cout << v << ", ";
+    }
+    std::cout << std::endl;
+  }
+
+  return 0;
+}