Learn Hardcore Japanese: inu no atama ha tiisai desu.

The particle の indicates possession or a descriptive relationship. Here 犬の頭 literally means “the dog’s head.” You can think of it like the English apostrophe-s (“dog’s head”).

What does は do in this sentence?

は is the topic marker. It marks 犬の頭 (“the dog’s head”) as the topic, telling the listener “As for the dog’s head….” After the topic comes your comment or description, which is 小さいです (“is small”).

Why is が not used here instead of は?

が marks the grammatical subject (often introducing new information or emphasis), whereas は marks the topic (what you’re talking about). In 犬の頭は小さいです, you’re stating a known or highlighted topic (“the dog’s head”) and then describing it. If you used が like 犬の頭が小さいです, it would feel more like you’re pointing out “It’s the dog’s head that happens to be small,” often in contrast to something else.

Why is the adjective 小さい placed after 頭 instead of before, as in English?

Japanese sentence structure for predicates is generally:
[Topic] は [Predicate] です.
Here, 小さい is the predicate (an i-adjective) describing the topic 犬の頭. In English you put adjectives before nouns (“small head”), but when you make a full sentence in Japanese you place the adjective after the topic. (When adjectives directly modify nouns attributively, though, they do come before, e.g. 小さい犬 “a small dog.”)

Why do we add です after the adjective 小さい?

小さい is an i-adjective and can stand alone as a predicate in plain form (小さい = “is small,” casual). Attaching です makes it polite: 小さいです = “is small” (polite). You cannot attach だ to an i-adjective (you’d just use the plain 小さい).

Can we omit です, and if so, what changes?

Yes. In casual speech you can say 犬の頭は小さい without です. It’s simply less formal. The meaning (“The dog’s head is small”) stays the same, but the tone becomes more everyday or familiar.

Why can’t we say 犬の頭は小さいだ?

I-adjectives like 小さい already include their own “ending,” so you never add だ to them. For nouns and na-adjectives you use だ (plain), but for i-adjectives you either leave them as is (plain) or add です (polite).

How would you say “a dog with a small head” (i.e. using this idea attributively)?

You’d move 小さい before 頭 and drop です, like this:
小さい頭の犬
Literally “small-headed dog.” (Here 小さい directly modifies 頭, and の犬 makes that phrase describe the dog.)

What’s the difference between 犬の頭は小さいです and 犬は頭が小さいです?

Both mean roughly “The dog’s head is small,” but the focus changes:

犬の頭は小さいです treats “the dog’s head” as one chunk topic.
犬は頭が小さいです treats “the dog” as topic, then says “(its) head (が) is small.”
The latter is more common if you want to talk about the dog and then describe its head among other possible traits.