Adjectives have three forms: positive (basic), comparative and superlative. Higher is the comparative form of the adjective high. The comparative form is normally used to compare things. When forming the comparative of short adjectives, e.g. new, you usually need to add the ending –er. Use the construction comparative adjective + than when comparing one thing with another:

This route is shorter than the other one.

The highest is the superlative form of the adjective high. The superlative form is normally used to express the highest degree of a given quality.  When forming the superlative of short adjectives, use the definite article the and add the ending –est:

Mount Everest is the highest mountain in the world.

If the adjective ends in a consonant + y, (e.g. ugly), change the y to i and add –er or –est:

• uglier
• the ugliest

When forming the comparative and superlative forms of adjectives that end in –e, add –r or –st:

• nicer
• the nicest

Note that –er/-est comparison is only used for short adjectives. Long adjectives, however, have different comparison. Long adjectives include adjectives with three or more syllables (e.g. beautiful), and also some two-syllable adjectives, e.g. adjectives ending in –ful, –ing or –less.

• Comparative of adjectives with three or more syllables: more + adjective:
  Nowadays it’s more convenient to book flights online.
• Superlative of adjectives with three or more syllables: the + most + adjective:
  This is the most chaotic airport I’ve ever been to.

To compare two things which have differing amounts of the same quality, use: more/less + adjective + than: Onboard shopping is less expensive than airport shopping.