Breasts are composed of two major tissue types:
1) glandular tissue - responsible for the mammary glands which produces milk
2) adipose tissue - fatty tissue
The adipose tissue is considered subcutaneous and lie under the skin of the breast. Glandular tissue is located in front of the pectoral muscle.The mammary glands are from cutaneous origin. They consist of a network of tubules called lactiferous ducts which are supported by loose connective tissue followed by dense connective tissue and adipose tissue. The dense tissue divides into septa between the ducts divide the mammary gland into lobes . These lobes are made up of lobules which contain alveoli. These alveoli also are composed of lactocytes which are secretory epithelial cells responsible for the secretion of breast milk . Structurally the alveoli are connected to the smaller ducts which join together to form larger ducts draining the lobules. The larger ducts also join into one milk duct for each lobe that eventually ends in the lactiferous sinus which is the opening of the nipple . The ducts themselves consist of stratified cuboidal epithelium which is made up of inner secretory cells and outer myoepithelial cells  while the inner sinus in the nipple is lined with a double layer of stratified cuboidal epithelium. As the outside of the nipple is reached the tissue gradually gives rise to keratinized stratified squamous epithelium .
Figure 2: Nonlactating breast showing lactiferous ducts, loose connective tissue, dense connective tissue and adipose tissue 
Figure 3: A closer look at a lactiferous duct 
The areola is covered with a thin layer of stratified squamous epithelium. This layer contains keratin and is continous over the entire breast, including the exterior of the nipple. The dermis, comprised of elastic connective tissue, extends deep into the skin and forms irregular dermal papillae .
Figure 4: A closer look at the nipple 
FACT OF THE DAY!!
Mammary glands resemble sweat glands and are actually derivatives of eccrine sweat glands