Inclusion Criteria:  Male or female, non-smoker (no use of tobacco or nicotine products within 3 months prior to screening), greater than or equal to (>=) 18 and less than or equal to (<=) 55 years of age, with body mass index (BMI) greater than (>) 18.5 and less than (<) 30.0 kilograms per meter square (kg/m^2) and body weight >=55 kilograms (kg) and <=100 kg for females and body weight >=60 kg and <=100 kg for males.  Healthy as defined by:  The absence of clinically significant illness and major surgery within 4 weeks prior to dosing. Participants vomiting within 24 hours pre-dose will be carefully evaluated for upcoming illness/disease. Inclusion pre-dosing of the patient in the study is at the discretion of the Investigator, depending on his/her clinical judgement. The absence of clinically significant history of neurological, endocrinal, cardiovascular, pulmonary, hematological, immunologic, psychiatric, gastrointestinal, renal, hepatic, and metabolic disease.  Non-childbearing potential female defined as:  Post-menopausal female (absence of menses for 12 months prior to the first study drug administration, bilateral oophorectomy or hysterectomy with bilateral oophorectomy at least 6 months prior to the first study drug administration); or Surgically sterile female (hysterectomy or tubal ligation at least 6 months prior to drug administration).  Females of childbearing potential who are sexually active with a male partner must be willing to use one of the following acceptable contraceptive methods throughout the study and for at least 90 days after the last study drug administration:  Simultaneous use of intra-uterine contraceptive device, without hormone release system placed at least 4 weeks prior to study drug administration, and condom for the male partner; Simultaneous use of diaphragm or cervical cap with intravaginally applied spermicide and male condom for the male partner, started at least 21 days prior to study drug administration;  Male participants who are not vasectomized for at least 6 months, and who are sexually active with a female partner of childbearing potential (childbearing potential females are defined as women that are neither post-menopausal nor surgically sterile) must be willing to use one of the following acceptable contraceptive methods from the first study drug administration until at least 90 days after the last study drug administration:  Simultaneous use of a male condom and, for the female partner, hormonal contraceptives used since at least 4 weeks or intra-uterine contraceptive device placed since at least 4 weeks; Simultaneous use of a male condom and, for the female partner, a diaphragm or cervical cap with intravaginally applied spermicide. Male participants (including men who have had a vasectomy) with a pregnant partner must agree to use a condom from the first study drug administration until at least 90 days after the last study drug administration. Male participants must be willing not to donate sperm until 90 days following the last study drug administration. Female participants must be willing not to donate ovules until 90 days following the last study drug administration. Participant's written informed consent obtained prior to any study-related procedure. Willingness and capability to comply with the requirements of the study and ability to understand the study procedures and the risks involved. Willing to take out dentures and mouth piercings for study procedures.  Exclusion Criteria:  Any clinically significant abnormality at physical examination, clinically significant abnormal laboratory test results or positive test for human immunodeficiency virus (HIV), hepatitis B, or hepatitis C found during medical screening. Clinically significant vital sign abnormalities (systolic blood pressure lower than 90 or over 140 millimeter of mercury [mmHg], diastolic blood pressure lower than 60 or over 90 mmHg, or heart rate less than 40 or over 100 beats per minute [bpm]) at screening. For eligibility purposes, not the mean value, but the two single measurements will be considered. Any of the following abnormalities on 12-lead ECG at screening. PR (PR interval) >210 millisecond (msec); QRS (QRS complex) >120 msec; QTcF >450 msec; any abnormality of cardiac rhythm other than sinus arrhythmia; abnormality of T-wave morphology that will impair the ability to measure the QT interval reliably. The averaged value of three ECGs 5 minutes apart from each other will be used; evaluations have to be used for the evaluation of the QTc interval requested by this exclusion criteria. Participants with history of sustained and non-sustained cardiac arrhythmias (ECG demonstrated), participants with a family history of sudden cardiac death and participants with a history of additional risk factors for TdP, heart failure, hypokalemia, LQTS).  Any of the following abnormal laboratory test values at screening or at baseline (Day -1) of Period 1:  Platelet count <125*10^9 per liter (/L) Absolute neutrophil count <1.2*10^9/L Participants who have cardiovascular condition such as, but not limited to unstable ischemic heart disease, New York Heart Association (NYHA) Class III/IV left ventricular failure, acute ischemic heart disease in the last year prior to study screening, which may impact the safety of the participant or the evaluation of the result of the study according to the Investigator's judgment; cardiovascular conditions should be discarded based on the results obtained on the ECG, medical examination and routine lab test. Positive urine drug screen, alcohol breath test or urine cotinine test at screening or at baseline (Day -1). History of anaphylaxis reaction or clinically significant drug hypersensitivity reaction (e.g., angioedema, Stevens-Johnson syndrome, Acute Generalized Exanthematous Pustulosis, Drug-induced hypersensitivity syndrome, Drug-induced neutropenia). History of allergic reactions to ITF2357, histone deacetylases (HDAC) inhibitors, or other related drugs, moxifloxacin, other quinolones, or to any excipient in the formulation. Positive pregnancy test at screening or at baseline (Day -1). Participants with a sorbitol intolerance or sorbitol malabsorption or have fructose intolerance. Current or recent (within 3 months of study drug administration) clinically significant gastrointestinal disease that can interfere with drug absorption. Gastrointestinal surgery that interferes with physiological absorption and motility (i.e., gastric bypass, duodenectomy) or gastric bands. History of significant alcohol abuse within 1 year prior to screening or regular use of alcohol within 6 months prior to the screening visit (more than 14 units of alcohol per week [1 unit = 150 milliliter [mL] of wine, 360 mL of beer, or 45 mL of 40 percent [%] alcohol]). History of significant drug abuse within 1 year prior to screening or use of soft drugs (such as marijuana) within 3 months prior to the screening visit or hard drugs (such as cocaine, phencyclidine [PCP], crack, opioid derivatives including heroin, and amphetamine derivatives) within 1 year prior to screening. Use of ITF2357 for a medical condition or in the context of another clinical trial within a period of 30 days prior to the first dosing. Participation in a clinical research study involving the administration of an investigational or marketed drug or device within 30 days prior to the first dosing, administration of a biological product in the context of a clinical research study within 90 days prior to the first dosing, or concomitant participation in an investigational study involving no drug or device administration.  Use of medications for the timeframes specified below, with the exception of medications exempted by the Investigator on a case-by-case basis because they are judged unlikely to affect the pharmacokinetic profile of the study drug or participant safety (e.g., topical drug products without significant systemic absorption):  Prescription medications within 14 days prior to the first dosing; OTC products (with the exception of the occasional use of acetaminophen [up to 2 grams [g] daily]) and natural health products (including herbal remedies, homeopathic and traditional medicines, probiotics, food supplements such as vitamins, minerals, amino acids, essential fatty acids, and protein supplements used in sports) within 7 days prior to the first dosing; Depot injection or implant of any drug within 3 months prior to the first dosing; Any drugs known to induce or inhibit hepatic drug metabolism (including St. John's wort) within 30 days prior to the first dosing. Donation of plasma within 7 days prior to dosing. Donation or loss of blood (excluding volume drawn at screening) of 50 mL to 499 mL of blood within 30 days, or more than 499 mL within 56 days prior to the first dosing. Breast-feeding participant. Inability to be venipunctured and/or tolerate catheter venous access; Inability or difficulty to swallow tablets or suspension. Any reason which, in the opinion of the Investigator, would prevent the participant from participating in the study. History or presence of other diseases, metabolic dysfunctions, physical examination findings, or any clinically relevant abnormal laboratory value at screening suggesting an unknown disease and requiring further clinical investigation or which may impact the safety of the participant or the evaluation of the result of the study according to the Investigator's judgment.