Links vs. Linke
In German, both Links and Linke relate to the direction left. However, they are different parts of speech and are not interchangeable. Links is an adverb that describes a direction or location, while Linke is a declined form of the adjective link or a noun.
Links
A1Links is an adverb. It answers the questions Where? (Wo?) or Where to? (Wohin?). It describes a direction or a location and, as an adverb, its form never changes.
Unser Haus ist das dritte von links.
(Our house is the third from the left.)
Bitte biegen Sie an der Ampel links ab.
(Please turn left at the traffic light.)
Der Supermarkt befindet sich links neben der Post.
(The supermarket is located to the left of the post office.)
Schau zuerst nach links und dann nach rechts.
(Look first to the left and then to the right.)
Politisch steht er eher links.
(Politically, he is more on the left.)
Linke
A2Linke is the declined form of the adjective link (left). Its ending changes to agree in gender, number, and case with the noun it modifies. Linke can also be a noun, referring to a left-wing person or the political Left.
Meine linke Hand ist eingeschlafen.
(My left hand has fallen asleep.)
Der linke Schuh ist mir zu eng.
(The left shoe is too tight for me.)
Die linke Fahrspur ist für die schnelleren Autos.
(The left lane is for the faster cars.)
Die Linke ist eine politische Partei in Deutschland.
(The Left is a political party in Germany.)
Als überzeugte Linke demonstrierte sie für den Frieden.
(As a convinced left-winger (female), she demonstrated for peace.)
Summary
In short: Use links as an adverb to indicate direction or position (turn left, on the left). It is invariable. Use linke (or other forms like linker, linkes, linken) as an adjective that must agree with the noun it describes (the left hand, the left shoe). Linke can also be a noun for a person or political party (The Left).