How can I make my enemy stay on the ground and collide with other objects?

In my script the enemy chases the player until it is close enough to attack, but they enemy doesn't stay on the ground and flies through walls. How can I make it obey gravity? here's my code:

 using UnityEngine;
 using System.Collections;
 using UnityEngine.UI;
 
 public class EnemyChase : MonoBehaviour {
 
     public Transform Player;
     public int MoveSpeed = 4;
     public int MinDist = 5;
     public int MaxDist = 10;
     public Slider healthBarSlider;
 
     bool attack;
 
     void Update() {
         //squares up
         transform.LookAt(Player);
         //chases player
         if (Vector3.Distance (transform.position, Player.position) <= MaxDist) {
             transform.position += transform.forward * MoveSpeed * Time.deltaTime;
             //stops doing damage
             attack = false;
             Debug.Log ("get over here and fight like a man!");
             //stops and attacks when close enough to player
             if(Vector3.Distance(transform.position,Player.position) <= MinDist) {
                 Debug.Log ("PEWEWPEWEPWEWPEPWP");
                 //starts doing damage
                 attack = true;
             }
         }
         //applies damage to player
         if (attack) {
             healthBarSlider.value -= 0.005f;
         } else if (healthBarSlider.value == 0) {
             //die
         } else {
             healthBarSlider.value += 0.0f;        
         }
     }
 }