**Core Concept**
Alveolar bone is a type of compact bone tissue that surrounds the roots of teeth and provides a firm attachment for the teeth within the jawbone. It is a critical component of the periodontium, which consists of the gingiva, periodontal ligament, cementum, and alveolar bone.

**Why the Correct Answer is Right**
The alveolar bone is composed of compact bone tissue that is rich in osteocytes and is highly vascularized. It is responsible for providing the structural support for the teeth and facilitating the transmission of forces from the teeth to the surrounding bone. The alveolar bone also plays a crucial role in the formation of the dental socket during tooth development and the resorption of the socket during tooth loss.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the alveolar bone is not a type of cancellous bone, which is characterized by its spongy texture and high surface area.
**Option B:** This option is incorrect because the periosteum is a fibrous membrane that covers the surface of bones, including the alveolar bone, but it is not the bone itself.
**Option C:** This option is incorrect because the periodontal ligament is a fibrous connective tissue that connects the tooth to the surrounding alveolar bone, but it is not a type of bone tissue.

**Clinical Pearl / High-Yield Fact**
The alveolar bone is highly dynamic and undergoes continuous remodeling throughout life in response to changes in occlusal forces and other factors. This process of bone resorption and formation is critical for maintaining the health and stability of the teeth.

**Correct Answer:** C.