the ability to understand and share the feelings of another.

According to Wikipedia...

Empathy is the capacity to understand or feel what another person is experiencing from within their frame of reference, i.e., the capacity to place oneself in another's position. There are many definitions for empathy that encompass a broad range of emotional states. Types of empathy include cognitive empathy, emotional empathy, and somatic (physical) empathy.

Important notes

• Empathy is not exclusively a human ability, it is shared by primates and likely other mammals as well. See the work of Frans de Waal, noted primate researcher.
• Empathy is distinct from pity. Pity is feeling that another is in trouble and in need of help as they cannot fix their problems themselves, often described as "feeling sorry" for someone. 
• Empathy is distinct form emotional contagion. Emotional contagion is when a person (especially an infant or a member of a mob) imitatively "catches" the emotions that others are showing without necessarily recognizing this is happening.

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