webpack-dev-server Cannot find module 'webpack'

I'm trying to use webpack-dev-server to run a simple program but I'm getting this error:

module.js:471
    throw err;
    ^

Error: Cannot find module 'webpack'
    at Function.Module._resolveFilename (module.js:469:15)
    at Function.Module._load (module.js:417:25)
    at Module.require (module.js:497:17)
    at require (internal/module.js:20:19)
    at Object.<anonymous> 
    at Module._compile (module.js:570:32)
    at Object.Module._extensions..js (module.js:579:10)
    at Module.load (module.js:487:32)
    at tryModuleLoad (module.js:446:12)
    at Function.Module._load (module.js:438:3)

I have installed webpack with following npm command

npm install --save-dev webpack

and I have the following configuration:

(webpack.config.js)
var webpack = require('webpack');
var path = require('path');

var BUILD_DIR = path.resolve(__dirname, 'client/public');
var APP_DIR = path.resolve(__dirname, 'client/app');

var config = {
  entery: APP_DIR + '/index.js',
  output: {
    path: BUILD_DIR,
    filename: 'bundle,js',
  },
  module: {
    loaders: [
      {
        test: /.jsx?$/,
        loader: 'babel-loader',
        exclude: /node_modules/,
        query: {
          presets: ['es2015', 'react']
        }
      }
    ]
  }
};

module.exports = config;

I have tried everything and I'm really lost. Does anyone have any idea?

npm install --save-dev webpack is not enough.

You also have to install the following:

npm install --save-dev webpack-dev-server 

And optionally, you can also install:

npm install --save-dev webpack-dev-middleware webpack-hot-middleware

I had the same problem, but I resolved by installing additional webpack-cli

npm install --save-dev webpack-cli