changing font family of all material-ui(version 1) components

You can change the font in material-ui@next library doing the following. Suppose in your <App /> which is defined like the following

// Material UI
import { MuiThemeProvider, createMuiTheme } from 'material-ui/styles';

const App = () => (
  <MuiThemeProvider theme={THEME}>
    <Provider store={store}>
      <Router history={appHistory} routes={Routes} />
    </Provider>
  </MuiThemeProvider>
 );

 ReactDOM.render(<App />, document.getElementById('app'));

In the theme prop for MuiThemeProvider you provide the following where

const THEME = createMuiTheme({
   typography: {
    "fontFamily": `"Roboto", "Helvetica", "Arial", sans-serif`,
    "fontSize": 14,
    "fontWeightLight": 300,
    "fontWeightRegular": 400,
    "fontWeightMedium": 500
   }
});

Then somewhere in your css or your main index.html file include this @import url('https://fonts.googleapis.com/css?family=Roboto:300,400,500,700');

For a list of all params you can give to createMuiTheme Default Theme Params Regarding the docs itself for changing the MuiTheme they are as follows. Themes Material UI Next

Regarding the <Reboot /> part you can have a look at the documentation here Material UI Reboot Details

**** UPDATES *****

Adding to the accepted answer by Adeel.

For the latest Material-UI(v4+) components, the imports, as well as MuiThemeProvider, have been changed.

So now in your App.js, do the following:

import { createMuiTheme } from '@material-ui/core/styles';
import { ThemeProvider } from '@material-ui/styles';
import './Styles/App.css';

const theme = createMuiTheme({
  typography: {
    fontFamily: [
      'Nunito',
      'Roboto',
      '"Helvetica Neue"',
      'Arial',
      'sans-serif'
    ].join(','),
  }
});

class App extends Component {
  render() {
    return (
      <ThemeProvider theme={theme}>
        <div className="App">
          <MainApp />
        </div>
      </ThemeProvider>
    );
  }
}

export default App;

Now for example, I've added the Nunito font. So I had to add the same to the App.css (which is being imported in App.js) in the following way:

@font-face {
  font-family: 'Nunito';
  font-style: normal;
  font-weight: 400;
  font-display: swap;
  src: local('Nunito Regular'), local('Nunito-Regular'), 
   url(https://fonts.gstatic.com/s/nunito/v11/XRXV3I6Li01BKofINeaBTMnFcQ.woff2) 
   format('woff2');
  unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, 
    U+02DC, U+2000-206F, U+2074, U+20AC, U+2122, U+2191, U+2193, U+2212, 
    U+2215, U+FEFF, U+FFFD;
}

This is now the preferred method:

const theme = createMuiTheme({
  typography: {
    fontFamily: [
      '-apple-system',
      'BlinkMacSystemFont',
      '"Segoe UI"',
      'Roboto',
      '"Helvetica Neue"',
      'Arial',
      'sans-serif',
      '"Apple Color Emoji"',
      '"Segoe UI Emoji"',
      '"Segoe UI Symbol"',
    ].join(','),
  },
});

As noted here: https://material-ui.com/customization/typography/