Advent and Lent are both seasons of expectant waiting. During Lent, Christians copy Jesus' time of austere preparation through self reflection, fasting, and study. Study may be done on one's own, eg: reading a suitable book or praying often, but is better done together by doing those things with others, either on a single occasion, or every week throughout the season of Lent.
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Austerity:
It's usual to take out of the church all flowers and adornments. High churches
(Anglican churches that copy parts of Roman Catholic practice), also wrap any crosses and statues depicting Jesus with a purple shroud, in deference to a passage in John's Gospel, in which Jesus hid himself from the authorities
(John 8:59).
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Self-reflection and fasting: This is similar to the self-reflection during the season of
Advent and is a time for bringing to mind one's failure to keep God's Laws and being sorry for it. Lent especially has an emphasis on being sorry
(penance); that is, on bringing to mind and being sorry for the things we do wrong
(which we call 'sin').
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Study: Many Christians attend a 'Lent Course' arranged locally or follow one of the many national courses that are published for that purpose, both as a penance
(giving up time to study) and in order to learn more about God, about themselves, and about their own faith, thereby copying Jesus' time of learning about himself and what God wanted for him.
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Fasting: This refers to abstaining from both food and festivities. Years ago it was common to abstain from food in more rigorous ways than we do today. People would go without food all day and not eat various foods at all during Lent, such as meat, eggs and alcohol - a vegetarian diet during Lent was not uncommon. Today most people in the west have relaxed those rules, but many still give up something as a sign of penance, such as chocolate, smoking, or alcohol. Many also refrain from going to parties or meetings in order to be symbolically alone, as Jesus was alone in the wilderness.