Learn Hardcore Russian: Я кладу книгу на верхнюю полку.

кладу is the 1st-person singular present tense of the imperfective verb класть, which emphasizes an ongoing or habitual action (“I am putting / I put regularly”).
положу is the 1st-person singular future tense of the perfective verb положить, which describes a single, completed action in the future (“I will put it”).

Why is книгу in the accusative case?

книгу is the direct object of кладу. In Russian, transitive verbs require their direct object to be in the accusative case. The noun книга (feminine) becomes книгу in singular accusative.

Why is верхнюю полку also in the accusative case?

The preposition на can govern either the accusative (for motion toward a place) or the prepositional (for static location). Since you’re placing the book onto the shelf (movement), верхняя полка is marked accusative feminine singular: верхнюю полку.

How do the adjective endings work in верхнюю полку?

верхнюю is the accusative singular feminine form of верхний (“upper/top”).
– Masculine/neuter adjectives have different endings; feminine adjectives ending in -ий change to -юю in the accusative.
It must agree in gender, number, and case with полка, which is feminine singular accusative (полку).

Could I use a different verb to express “put” in this sentence?

Yes. Depending on context and aspect:
– положить (perfective) → “Я положу книгу на верхнюю полку” (I will put the book… – completed future).
– поставить (perfective, “to set upright”) → “Я поставлю книгу на верхнюю полку” (if you mean standing it up).
– класть stays imperfective → “Я кладу книгу …” (I am in the process of putting / habitually put).

Is the word order here fixed, or can I change it?

Standard neutral order is S–V–O–adv: Я кладу книгу на верхнюю полку.
Russian is relatively flexible due to case endings. For emphasis you could say:
– Книгу я кладу на верхнюю полку (emphasizes книга).
– На верхнюю полку я кладу книгу (emphasizes the shelf).

How is на used here, and can it ever take a different case?

– When на indicates movement onto something, it takes the accusative (as here).
– When it indicates location (e.g. “the book is on the shelf”), it takes the prepositional: на верхней полке.

Where is the stress in книгу and полку?

книгу – stress on the first syllable: KNI-gu.
полку – stress on the first syllable: POL-ku.