Hi Niwantha :) I will try to explain the difference by using examples. "Undermine" means to go against something or someone (a synonym would be "to subvert"). For example, a sentence could be "The man undermined his boss' authority". This would mean that the man went against his bosses wishes. It also has connotations of "going behind someone's back to subvert their plans". "Underestimate" means to assume that someone is not as capable at something than they actually are. For example, in a fight, one person might "underestimate" his opponent's strength, believing him to be weaker than he actually is. The word "estimate" means to assume the value or ability of something, so to underestimate would mean to assume an estimate far below what something is worth. For example if someone was looking to buy plane tickes and believed they would be around $1000 but in fact they were $3000 then that person would have "underestimated" the cost of the plane ticket. I hope I helped and my explanations weren't too confusing. Let me know if you need anything clarified! :)