John Robinson (1575-1625) was the pastor of the Pilgrims after their removal to Holland in 1607-8, and many of his writings survive--giving us a direct view of the Pilgrims religious beliefs and theology.    

The Pilgrims' separatist movement can be directly traced back to John Calvin (1509-1564) and Calvinism, from which also descends Puritanism and Presbyterianism.  The Pilgrims' separatist movement sprung up from primarily Nottinghamshire, where Richard Clyfton and John Robinson, both Cambridge alumni, began their preaching.  Beginning in 1604 with the ascention of King James I, the persecution of Protestants increased, and the members of Clyfton and Robinson's church had to meet secretly, and were hunted continually by authorities--and when caught, thrown in jail.  By 1607, they could no longer take the persecution, and made their escape to Amsterdam, Holland, and a year later moved to Leyden where they established their congregation.  

In addition to John Robinson, William Bradford and Edward Winslow have added their own remarks to various theological debates of their day.  Below is a basic outline of some of these religious beliefs supported and practiced by the Leyden Pilgrims.  For those who are interested, the Pilgrims used John Calvin's Geneva translation of the Bible, nicknamed the "Breeches Bible".    

Predestination.  
The Pilgrims believed that before the foundation of the world, God predestined to make the world, man, and all things.  He also predestined, at that time, who would be saved, and who would be damned.  Only those God elected would receive God's grace, and would have faith.  There was nothing an individual could do during their life that would cause them to be saved (or damned), since God had already decided who was going to be saved before the creation of the world. However, God would not have chosen blatant sinners to be his elect; and therefore those who were godly were likely to be the ones God elected to be saved.  For more information, see: A Defence of the Doctrine Propounded by the Synod of Dort, by John Robinson, (1624). 

Sacraments and Popery.
To the Pilgrims, there were only two sacraments: baptism and the Lord's Supper.  The other sacraments (Confession, Penance, Confirmation, Ordination, Marriage, Confession, Last Rites) of the Catholic and Anglican churches were inventions of man and were therefore not Holy.  The Pilgrims opposed the mass, and considered marriage a civil affair (not a religious sacrament).  The legitimacy of the pope, the saints, and the church hierarchy was rejected, as was the veneration of relics.  Icons and religious symbols such as crosses, statues, stain-glass windows, fancy architecture, and other worldly manifestations of religion were rejected. 

Church Organization.
The church of the Pilgrims was organized around five officers: pastor, teacher, elder, deacon, and deaconess (sometimes called the "church widow").  However, none of the five offices was considered essential to the church.  The Pastor was an ordained minister whose responsibility was to see to the religious life of the congregation.  John Robinson was the pastor of the Pilgrims, but never was able to get to America before his death in 1625.  The Teacher was also an ordained minister who was responsible for the instruction of the congregation.  The Pilgrims apparently never had anyone to fill that position.  The Elder was a lay-person responsible for church government, and he was also the church's eyes and ears, assisting the Pastor and Teacher in admonishing the congregation.   See: A Just and Necessary Apology of Certain Christians, by John Robinson (1625), chapter 9, "Of the Ecclesiastical Presbytery". William Brewster was the Elder for the Plymouth church.  The Deacon collected offerings, and attended to the needs of the poor and elderly.  John Carver and Samuel Fuller both were deacons during their life.  The Deaconess attended the sick and poor, and often played the role of mid-wife as well.  The Deaconess of the early Plymouth church is not named, but may have been Bridget Fuller.  The church building itself had no significance to the Pilgrims, and was usually called simply the "meetingplace" or "meetinghouse".  The meetinghouse was kept drab, and had no religious depictions or icons.  Starting about the summer of 1622, the fort served as the Pilgrims meetinghouse.  The Pilgrim men brought loaded guns to church in case they were attacked during services.   

Infant Baptism.
The Pilgrims believed baptism was the sacrament which wiped away Original Sin, and was a covenant with Christ and his chosen people (as circumcision had been to God and the Israelites), and therefore children should be baptized as soon as practical.  See: Of Religious Communion, Private and Public, by John Robinson (1614).  This was in opposition to the Anabaptists, who believed that baptism was essentially an initiation ceremony into the churchhood of believers, and therefore could only be administered to believing adults who understood the meaning of the ceremony.  The Pilgrims believed that "Baptism now, as circumcision of old, is the seal of the covenant of God".  They further believed that at least one parent must be of the faith for the child to be baptized into the church.  See: A Just and Necessary Apology of Certain Christians, by John Robinson (1625). 

Holy Days and Religious Holidays.
The Pilgrims faithfully observed the Sabbath, and did not work on Sunday.  Even when the Pilgrims were exploring Cape Cod, to the Mayflower crew's dismay, they stopped everything and stayed in camp on Sunday to keep the Sabbaths.  See: Mourt's Relation (1622), chapter 1.  The Pilgrims did not celebrate religious holidays--Christmas and Easter being the prime examples.  These holidays were invented by man to memorialize Jesus, and are not prescribed by the Bible and therefore cannot be Holy.  "It seems too much for any mortal man to appoint, or make an anniversary memorial".  See: A Just and Necessary Apology of Certain Christians by John Robinson (1625) chapter 5; and Of Plymouth Plantation by William Bradford, chapter 12. 

Marriage.
The Pilgrims considered marriage a civil affair, not to be handled by the church ministers but instead by civil magistrates.  See: Of Plymouth Plantation, Ch. 12. Marriage was a contract, mutually agreed upon by a man and a woman.  Marriage was ordained by God for the benefit of man's natural and spiritual life.  Not getting married (and thus remaining a virgin) was not considered a sign of piety.  Marriages were considered important for two main reasons: procreation of children, and to avoid the sin of adultery.  The important characteristics to find in the proper spouse, according to Robinson, are (1) godliness, and (2) similarity--in age, beliefs, estate, disposition, inclinations, and affections.  In the marriage, "the wife is specially required a reverend subjection in all lawful things to her husband", and the husband is "to give honour to the wife", and the Lord requires "the love of the husband to his wife must be like Christ's to his church".  See: Observations Divine and Moral, by John Robinson (1628), chapter 59 "Of Marriage". 

Education of Children, and Discipline.
The Pilgrims believed that in the child's early years, the mother was the most important educator.  But as the child grew, the father became the more important figure--from the father they are to learn manners, wisdom, and authority.  The Pilgrims believed that children needed to be disciplined "with the rod" when necessary, as the Bible proclaims in Proverbs 13:24 and 22:15.  Children were also expected to learn from the husband's disciplining of his wife--a wife was to be disciplined just as the children were disciplined when she disobeyed her husband or sinned against God.  See Observations Divine and Moral (1624) by John Robinson, Chapter 60 "Of Children and their Education".  The Pilgrim's distinction between beating a wife, and disciplining a wife, is akin to the modern-day distinction between beating a child and spanking a child.  The standard court-administered punishment for wife-beating was a public whipping, which is certainly more severe than the modern "punishment".  None of the Mayflower passengers were ever accused of wife-beating.  Education was thought very important, but in early years of the Plymouth Colony there was not enough time or qualified individuals to teach.  All children, boys and girls both, were taught to read (because reading the Bible was something everyone needed to be able to do).  Writing, however, was not taught to girls, and in fact many boys never learned to write either.  If the situation required, writing was a skill that could be learned fairly easily by someone who already knew how to read. 

SOURCES: 
1.  The Works of John Robinson, Pastor of the Pilgrims.  Edited by Robert Ashton (London, 1851). 3-Volumes. 
 2.  The Reformation: A Narrative History Related by Contemporary Observers and Participates, by Hans Hillerbrand (Grand Rapids, repr. 1994).   
3.  Reformation Europe, by De Lamar Jensen (Lexington, 1992). 
4.  Of Plymouth Plantation, by William Bradford. (written 1630-1654). 
5.  Mourt's Relation: A Journal of the Pilgrims at Plymouth (London, 1622).