
die Sympathie
liking
A feeling of affection and goodwill toward a person that makes you like them.
Ich hatte von Anfang an eine große Sympathie für meine neue Kollegin.
I felt a strong liking for my new colleague from the very beginning.
liking / sympathy
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liking
A feeling of affection and goodwill toward a person that makes you like them.
Ich hatte von Anfang an eine große Sympathie für meine neue Kollegin.
I felt a strong liking for my new colleague from the very beginning.

sympathy
A feeling of compassion and understanding for someone in a difficult situation.
Er zeigte seine Sympathie für die Opfer der Flutkatastrophe durch eine großzügige Spende.
He showed his sympathy for the victims of the flood disaster through a generous donation.
Although it sounds similar, 'Sympathie' does not always mean the same thing as the English 'sympathy'. In German, it often simply describes liking a person (affection), while 'sympathy' usually means compassion in a bad situation.
Ich finde, der neue Chef ist eine gute Wahl, ich habe sofort Sympathie für ihn empfunden.
I think the new boss is a good choice; I felt an immediate liking for him.
The word contains the root '-pathie', which means 'feeling' or 'suffering'. You can also find this root in words like 'Antipathie' (aversion), 'Empathie' (the ability to put oneself in someone else's position), and 'Apathie' (apathy).
Seine Antipathie gegen laute Musik ist bekannt.
His aversion to loud music is well known.
If you want to express that you like someone, the fixed structures are 'Sympathie für jemanden haben' (to have a liking for someone) or 'Sympathie für jemanden empfinden' (to feel a liking for someone). The preposition 'für' is always followed by the accusative.
Sie hat eine große Sympathie für Menschen, die ehrlich sind.
She has a strong liking for people who are honest.
In the context of misfortune, suffering, or victims, 'Sympathie' means sympathy or compassion. Typical verbs in this context are 'seine Sympathie zeigen' (to show one's sympathy) or 'seine Sympathie ausdrücken' (to express one's sympathy).
Der Politiker drückte den Familien der Opfer seine tiefe Sympathie aus.
The politician expressed his deep sympathy to the families of the victims.
pity / compassion
Mitleid and Sympathie can both express an understanding response to a difficult situation. Mitleid is directed primarily at the suffering and can convey a certain distance. Here, Sympathie emphasizes a benevolent understanding of the person and their situation.

Nach seiner Niederlage empfand Mia Sympathie für den offen enttäuschten Bewerber.
After his defeat, Mia felt sympathy for the applicant, who was openly disappointed.
Nach seiner Niederlage empfand Mia Mitleid mit dem enttäuschten Bewerber.
After his defeat, Mia felt pity for the disappointed applicant.