What were the main beliefs and values of Shakespeare's era?

It is important to note that during Shakespeare's lifetime, there were two monarchs ruling in England.

Elizabeth I came to the throne at the age of twenty-five, following "Bloody Mary's" disastrous and horrific three-year reign. (The two women were half-sisters, but very different. Mary was strongly Catholic and had serious issues because of her father's—Henry VIII—break from the Catholic Church and his divorce of his Catholic wife, Mary's mother.) Mary had spent most of her reign persecuting and murdering Protestants.

This is important because Elizabeth (until now the longest reigning monarch in her country's history, and a woman) chose to tolerate Catholics to some extent. Mass was forbidden. The Queen's religion favored and required.

Queen Elizabeth made attendance at Church of England services mandatory, even though many church-goers had to travel long distances. People who did not attend—for any reason except illness—were punished with fines.

Overall, the people had a strong belief in God. 

During [Elizabeth I’s] 45-year reign, London became a cultural and commercial center where learning and literature thrived.

The arts flourished. Stage presentations were open to all classes, so the masses enjoyed and valued the theater. The theater was a focal point of society for many reasons. It was the only place where members of all classes were present. Social rank was a value of the society and members of the Elizabethan society easily recognized one's standing. This is evident with Shakespeare's characters in a play:

Many of Shakespeare's characters carried titles that—in the Bard's time—would have immediately told audience members a lot about that person's rank, importance, and authority over his peers. 

It was through plays like Shakespeare's where we find important elements regarding the beliefs of the time. Specifically, people during Shakespeare's time believed in the supernatural. This included ghosts, witches, fairies, changelings, etc. It is interesting to note that up until Shakespeare's time, these creatures were feared and blamed for all kinds of problems that people experienced. (For example, if the water dipper was missing, the fairies had taken it.) In Shakespeare's Hamlet, one reason Hamlet does not immediate avenge his father's murder is because he is not certain if the Ghost is truly the spirit of his deceased father or a servant of the devil, sent to win his immortal soul to its eternal damnation. This is especially important because Hamlet's uncle (the murderer) is now king and it was believed by the people of Shakespeare's time that regicide was a mortal sin.

Shakespeare used these beliefs to add to the suspense and excitement of his plays. Macbeth is destroyed because he fraternizes with witches, who describe before the audience how they only want to destroy him. On the other hand, Shakespeare's A Midsummer Night's Dream is a wonderful comedy about how the lives of young lovers—and a small band of actors—are trifled with for the amusement of the King and Queen of the Fairies. Shakespeare introduced the idea that fairies were not necessarily nasty (as they had been perceived for many years prior), but could be playful and sympathetic to a human's plight.

While people of Elizabeth I's era believed in witches, their persecution was limited. However, when James I ascended to the throne upon Elizabeth I's death, he was much more fanatical. He even wrote a book entitled Daemonologie, which was said to be based upon his own experiences. His persecution of witches was much greater than Elizabeth's so we can infer that whatever might have taken place in theaters to improve the image of some members of the supernatural realm, the fear of witches and servants of the devil had not changed, remaining a strong part of society's belief system.

Values of Shakespeare's time rested a great deal upon one's social standing. Royalty was afforded more latitude, freedom and tolerance than were those of lower social standing. If one had a privileged position in England, he or she had more value. 

["Values"] describes individual or personal standards of what is valuable or important.

English society during this time saw to the needs of those who had money and power. The poor were generally of no consequence: they had no rights in the face of landowners and the nobility. It would be many years before they were given representation with regard to health, sanitation, child-endangerment, etc.

Women had little value. A good wife was an obedient, hardworking, uncomplaining woman who was able to have children and keep house. Even among the nobles, women were expected to provide their husband with an heir. This belief was based upon primogeniture: that all of a man's goods and his title would pass on to his son. And the eldest son was the most valued, while second and third sons would often become soldiers or join the Church.

Education was of importance, but only for men of substance. Women of noble families might be educated. In the middle class, women were generally educated at home, most especially in how to sing, sew, manage a household, and entertain. Boys would be placed in an apprenticeship to learn a trade. For the poor, the option of begin educated was non-existent. For those who were destitute, life was drudgery. For women of poverty, life was often short—especially because of the dangers of childbearing.

As is often the case today, many people during Shakespeare's time believed in God. The people's belief in "the system" depended upon the success of who sat on the throne. During Shakespeare's time, men were valued more than women and education was generally reserved for the elite.

What is the socio-cultural context of Shakespeare's era?

Shakespeare wrote during the reign of Queen Elizabeth I, which we call the Elizabethan period. Prior to the Elizabeth period, England had been in a state of religious turmoil and financial decay. Elizabeth's father, King Henry VIII, had broken from the Catholic Church. As a consequence Catholic monasteries in England had been demolished, leaving many homeless. When Elizabeth's half-sister Queen Mary I ascended the throne, she re-instated the Catholic Church, leading to the persecution of anyone who sided with her late father's Protestant Church and a great deal of bloodshed. In addition, Queen Mary I married Spain's King Phillip II, who was at war with Italy, and Mary used England's royal treasury to fund Phillip's wars. Hence, when Queen Elizabeth ascended the throne, the English treasury was nearly broke, and many homeless and beggars wandered the streets.

Nevertheless, under Elizabeth, England's economic and social structure was able to recover. First, she put an end to all religious hostility. Then, she focused on stabilizing the economy. Under Elizabeth, due to Nicholas Hilliard's talents, the miniature portrait market began to thrive, along with the wool industry. There were also booms in the architectural and iron industries. New mining industries also began as tin and copper began to be mined in Cornwall and Cumberland respectively (Tennessee State University, Taylor, "Elizabethan Economy").

As England's economic and social well-being stabilized and prospered, the Renaissance era that flourished in Italy now also flourished in England, ushering in new desires for education, art, and culture and a new philosophical outlook. With more money, citizens had more financial ability and leisure to indulge in education, with an emphasis in studying science and a return to studying the Classics. A return to studying Greek and Roman Classics was especially made possible due to Elizabeth's stable break from the Roman Catholic Church; no longer were citizens forbidden to study the masterpieces of pagan Greek and Roman philosophers and writers.

The benefits of England's prosperity during the Renaissance especially shows up in Shakespeare's writings, which are full of historical, philosophical, and mythological references.