With express mount routers route and list routes of router.

express-routers-routes-list.js

const express = require('express');
const app = express();
const router = express.Router();

router.get('/pets/cats', (req, res) => {
  res.send('10 cats');
});

router.get('/pets/dogs', (req, res) => {
  res.send('5 dogs');
});

router.post('/pets/dogs', (req, res) => {
  res.send('A puppy added');
});

router.get('/wild/tigers', (req, res) => {
  res.send('1 tiger');
});

app.use('/animals', (req, res, next) => {
  // res.send('come later');
  next();
}, router);

router.stack.forEach(route => {
  Object.keys(route.route.methods).forEach(method => {
    console.log('%s %s', method, route.route.path );
  })  
});

app.listen(3000);