A summary offence or petty offence is a violation in some common law jurisdictions that can be proceeded against summarily, without the right to a jury trial and/or indictment (required for an indictable offence).
In Canada, summary offences are referred to as summary conviction offences. As in other jurisdictions, summary conviction offences are considered less serious than indictable offences because they are punishable by shorter prison sentences and smaller fines. These offences appear both in the federal laws of Canada and in the legislation of Canada's provinces and territories. For summary conviction offences that fall under the jurisdiction of the federal government (which includes all criminal law), section 787 of the Criminal Code specifies that, unless another punishment is provided for by law, the maximum penalty for a summary conviction offence is a sentence of 2 years less a day of imprisonment, a fine of $5,000 or both.
As a matter of practical effect, some common differences between summary conviction and indictable offences are provided below.
In Hong Kong, trials for summary offences are heard in one of the territory's Magistrates' Courts, unless the defendant is accused with other indictable offence(s). Typical examples for summary offences in Hong Kong include possession of a simulated bomb, drunkenness, taking photograph in courts, careless driving and pretending to be a public officer. 
In relation to England and Wales, the expression "summary trial" means a trial in the magistrates' court. In such proceedings there is no jury; the appointed judge, or a panel of three lay magistrates, decides the guilt or innocence of the accused. Each summary offence is specified by statute which describes the (usually minor) offence and the judge to hear it. A summary procedure can result in a summary conviction. A "summary offence" is one which, if charged to an adult, can only be tried by summary procedure. Similar procedures are also used in Scotland.
Certain offences that may be tried in a Crown Court (by jury) may be required to be tried summarily if the value involved is small; such offences are still considered either way offences, so are not thereby "summary offences" in the meaning of that term defined by statute. Contrariwise, certain summary offences may in certain circumstances be tried on indictment along with other offences that are themselves indictable; they do not thereby become "indictable offences" or "either way offences" but remain "summary offences", though tried by jury.
By a summary proceeding I mean principally such as is directed by several acts of parliament (for the common law is a stranger to it, unless in the case of contempts) for the conviction of offenders, and the inflicting of certain penalties created by those acts of parliament. In these there is no intervention of a jury, but the party accused is acquitted or condemned by the suffrage of such person only, as the statute has appointed for his judge. An institution designed professedly for the greater ease of the subject, by doing him speedy justice, and by not harassing the freeholders with frequent and troublesome attendances to try every minute offence. But it has of late been so far extended, as, if a check be not timely given, to threaten the disuse of our admirable and truly English trial by jury, unless only in capital cases.
In the United Kingdom, trials for summary offences are heard in one of a number of types of lower court. For England and Wales this is the Magistrates' Court. In Scotland, it is the Sheriff Court or Justice of the peace court, depending on the offence (the latter being primarily for the most minor of offences). Northern Ireland has its own Magistrates' Court system.
In United States federal and state law, "there are certain minor or petty offenses that may be proceeded against summarily, and without a jury". These can include criminal and civil citations, where a person may be charged with a criminal or non-criminal infraction without the need of a physical arrest, such as in cases of non-violent fineable violations, crimes that carry little incarceration time, or non-criminal acts such as speeding. Any crime that is punishable by the controlling law for more than six months of imprisonment must have some means for a jury trial. Some states, such as California, provide that all defendants are entitled to a jury trial (irrespective of the nature of their offenses). In any case, for summary criminal offenses in the United States, convictions can still show as such on a criminal record.
Contempt of court is considered a prerogative of the court, as "the requirement of a jury does not apply to contempts committed in disobedience of any lawful writ, process, order, rule, decree, or command entered in any suit or action brought or prosecuted in the name of, or on behalf of, the United States". There have been criticisms over the practice. In particular, Supreme Court Justice Hugo Black wrote in a 1964 dissent: "It is high time, in my judgment, to wipe out root and branch the judge-invented and judge-maintained notion that judges can try criminal contempt cases without a jury."
In Pennsylvania, for example, all defendants charged with misdemeanors enjoy a right to counsel regardless of the sentence imposed, only those charged with 'summary offenses' (violations not technically considered crimes and punishable by no more than 90 days' imprisonment, ... may receive a suspended sentence uncounseled. (Typical 'summary offenses' in Pennsylvania include the failure to return a library book within 30 days... and fishing on a Sunday ...(citations omitted) (emphasis added).
In Pennsylvania, for example, all defendants charged with misdemeanors enjoy a right to counsel regardless of the sentence imposed, only those charged with 'summary offenses' (violations not technically considered crimes and punishable by no more than 90 days' imprisonment, ... may receive a suspended sentence uncounseled. (Typical 'summary offenses' in Pennsylvania include the failure to return a library book within 30 days... and fishing on a Sunday ...(citations omitted).
During a hearing on remand, Adefemi acknowledged several other convictions and arrests, including the circumstances surrounding Georgia Citation Number 0129, under which Adefemi received a citation for a weapons violation.