React with ES7: Uncaught TypeError: Cannot read property ‘state’ of undefined

Make sure you’re calling super() as the first thing in your constructor.

You should set this for setAuthorState method

class ManageAuthorPage extends Component {

  state = {
    author: { id: '', firstName: '', lastName: '' }
  };

  constructor(props) {
    super(props);
    this.handleAuthorChange = this.handleAuthorChange.bind(this);
  } 

  handleAuthorChange(event) {
    let {name: fieldName, value} = event.target;

    this.setState({
      [fieldName]: value
    });
  };

  render() {
    return (
      <AuthorForm
        author={this.state.author}
        onChange={this.handleAuthorChange}
      />
    );
  }
}

Another alternative based on arrow function:

class ManageAuthorPage extends Component {

  state = {
    author: { id: '', firstName: '', lastName: '' }
  };

  handleAuthorChange = (event) => {
    const {name: fieldName, value} = event.target;

    this.setState({
      [fieldName]: value
    });
  };

  render() {
    return (
      <AuthorForm
        author={this.state.author}
        onChange={this.handleAuthorChange}
      />
    );
  }
}