Add a Widget to Display Categories

<?php
class Category_List_Widget extends WP_Widget {

    function __construct() {
        parent::__construct(
            'category_list_widget',
            __('Category List Widget', 'text_domain'),
            array('description' => __('Displays a list of categories.', 'text_domain'))
        );
    }

    public function widget($args, $instance) {
        $title = !empty($instance['title']) ? $instance['title'] : __('Categories', 'text_domain');

        echo $args['before_widget'];
        if (!empty($title)) {
            echo $args['before_title'] . $title . $args['after_title'];
        }

        echo '<ul>';
        $categories = get_categories();
        foreach ($categories as $category) {
            echo '<li><a href="' . get_category_link($category->term_id) . '">' . $category->name . '</a></li>';
        }
        echo '</ul>';

        echo $args['after_widget'];
    }

    public function form($instance) {
        $title = !empty($instance['title']) ? $instance['title'] : __('Categories', 'text_domain');
        ?>
        <p>
            <label for="<?php echo $this->get_field_id('title'); ?>"><?php _e('Title:'); ?></label>
            <input class="widefat" id="<?php echo $this->get_field_id('title'); ?>" name="<?php echo $this->get_field_name('title'); ?>" type="text" value="<?php echo esc_attr($title); ?>">
        </p>
        <?php
    }

    public function update($new_instance, $old_instance) {
        $instance = array();
        $instance['title'] = (!empty($new_instance['title'])) ? strip_tags($new_instance['title']) : '';
        return $instance;
    }
}

function register_category_list_widget() {
    register_widget('Category_List_Widget');
}
add_action('widgets_init', 'register_category_list_widget');