Inclusion Criteria:  Patients must be 1 and < 26 years of age at the time of enrollment, and able to swallow brigatinib tablets at the time of enrollment, with a minimum weight of 10 kg. Note: for phase 1 only patients ≤18 years old will be eligible, A liquid formulation for children with a weight lower than 10 kg or for those that cannot swallow tablets is in development. Patients must have a confirmed diagnosis of cancer histologically at baseline. In patients where a repeat biopsy at relapse (or moment of refractory disease) is considered not feasible by the treating physician, archived material from diagnosis needs to be available for central review. Patients are required to provide prior results showing an activating ALK aberration in the tumor per local laboratory results, and material needs to be available for central laboratory confirmation of ALK status. For ALK+ ALCL, detection of ALK with immunohistochemistry (IHC) is sufficient for inclusion, all others require molecular evidence of a ALK fusion gene or mutation by FISH, PCR or NGS. ALK detection will be confirmed centrally with FISH.  For Phase 1:  Patients with ALCL must be relapsed/refractory or intolerant to standard therapies. Refractory disease for ALCL is defined as:  o no response to ALCL99/other standard of care chemotherapy (SD or PD of measurable lesions), and/or  o MRD-positivity by qualitative PCR for NPM-ALK prophase after one block ALCL99/other standard of care chemotherapy (before the second course of chemotherapy).  Patients with relapsed/refractory (R/R) IMT must not be suitable for curative surgical resection without causing mutilation. Newly diagnosed patients with unresectable ALK+ IMT, or when surgery would imply severe mutilation may also be included, as well as metastatic disease. Patients with other solid tumors (excluding IMT) must have relapsed or refractory disease.  For Phase 2, patients must have measurable and/or evaluable disease:  Patients with ALCL must be relapsed/refractory. Refractory disease for ALCL is defined as:  no response to ALCL99/other standard of care chemotherapy (SD or PD of measurable lesions), and/or MRD-positivity by qualitative PCR for NPM-ALK prophase after one block ALCL99/other standard of care chemotherapy (before the second course of chemotherapy). Patients with R/R IMT Relapsed/refractory ALK+ IMT, or newly diagnosed, including advanced and metastatic, ALK+ IMT which cannot be surgically resected without causing mutilation Performance Status: Karnofsky performance status ≥40% for patients >16 years of age or Lansky Play Scale ≥40% for patients ≤16 years of age. Patients must not be receiving other investigational medications (defined as medicinal products not yet approved for any indications, including alternative/herbal therapies) within 30 days of first dose of study drug or while on study.  For patients receiving prior therapy:  Patients who already received previous treatment with ALK inhibitors except for brigatinib can be included in this study. Patients must have recovered to Grade <2 NCI CTCAE v5.0 or to baseline, from any nonhematologic toxicities (except alopecia and peripheral neuropathy) due to previous therapy. Patients who relapsed while receiving cytotoxic therapy: at least 14 days must have passed since the completion of the last dose of chemotherapy before the first dose of brigatinib can be given. Patients who have experienced relapse after a prior HSCT are eligible, provided they have no evidence of acute or chronic graft-versus-host disease (GVHD), are not receiving GVHD prophylaxis or treatment, and are at least 45 days posttransplant at the time of enrollment. Hematopoietic growth factors: before the first dose of brigatinib, at least 7 days must have passed since completion of therapy with granulocyte colony-stimulating factor or other growth factors, and at least 14 days must have passed since completion of therapy with pegfilgrastim.  Biologics and Targeted Therapies:  o Immunotherapy: Before the first dose of brigatinib, at least 30 days must have passed after the completion of any type of immunotherapy, (i.e. monoclonal antibodies [anti-PD1/PDL1], tumor vaccines, chimeric antigen receptor [CAR] T cells, etc.).  o Other: before the first dose of brigatinib, at least 7 days must have passed since the last dose of a biologic agent. For agents that have known adverse events (AEs) occurring beyond 7 days after administration, this period must be extended beyond the time during which AEs are known to occur. The duration of this interval must be discussed with the sponsor's medical monitor/designee.  o Immunosuppressive therapy: Before the first dose of brigatinib, at least 14 days must have passed after the completion of immunosuppressive therapy (including regimens following stem cell transplant).  o For symptomatic patients that urgently need relief (i.e. airway obstruction), therapeutic doses of corticosteroids may be administered for a short course (up to 5 days).  o Radiotherapy (XRT): No washout period is necessary for radiation given to any extramedullary site other than the CNS and lungs; ≥45 days must have passed if patient received prior total body irradiation or craniospinal or cranial XRT; ≥28 days must have passed if patient received radiotherapy to the lung. For patients receiving XRT to both lungs, or in case of stereotactic radiotherapy, the PIs should be consulted before inclusion.  Patients must meet the organ function and system function requirements as stated below:  Patients must have adequate renal and hepatic function as indicated by the following laboratory values:  o Patient's serum creatinine must be ≤ 1.5 x institutional upper limit of normal (ULN) according to age. If the serum creatinine is greater than 1.5 x institutional ULN, the patient must have a radioisotope GFR ≥ 70mL/min/1.73m2  Adequate liver function defined as: direct bilirubin ≤1.5 times the upper limit of normal (ULN) for age AND AST and ALT must be ≤5 times the ULN for age (unless related to involvement of the liver or histiocytic/macrophage inflammatory process).  No clinical, radiological or laboratory evidence of pancreatitis, including o Serum lipase must be <2 × the ULN, and  o Serum amylase must be <2 × the ULN.  Absolute neutrophil count: ≥0.75 × 10 9/L, except in case of macrophage activation syndrome (MAS) or bone marrow involvement. Platelet count o In phase 1: Platelet count: ≥75 × 10^9/ L, except in case of MAS or bone marrow involvement o In phase 2: : Platelet count: ≥75 × 10^9/ L, except in case of MAS or bone marrow involvement. For patients post SCT, platelet count ≥50 × 10^9/ L is accepted.Hemoglobin ≥8 g/dL or 5.0 mmol/L (red blood cell [RBC] transfusions to achieve this value are allowed with the condition that the patient has no signs of active bleeding or hemolysis). Adequate cardiac function defined as shortening fraction ≥27% by echocardiogram OR left ventricular ejection fraction of ≥50% by multigated acquisition scan. Normal QT interval corrected per Fridericia method (QTcF) on screening electrocardiogram (ECG), defined as QTcF of ≤450 ms. Have a life expectancy of ≥3 months. Female patients of childbearing potential must have a negative urine or serum pregnancy test confirmed prior to enrollment. Female patients with infants must agree not to breastfeed their infants while on this study.  Contraception:  • Male and female patients of child-bearing potential must agree to use, an effective method for male and highly effective method for female, of contraception approved by the investigator during the study, following the CTFG recommendations, for at least 8 months for females and for at least 5 months for males after the last dose of brigatinib.  • Highly effective methods of contraception include (but not exclusively) the following contraceptive methods:  o combined (estrogen- and progestogen-containing) hormonal contraception associated with inhibition of ovulation  progestogen-only hormonal contraception associated with inhibition of ovulation intrauterine device (IUD), intrauterine hormone-releasing system (IUS), sexual abstinence.  Voluntary written informed consent according to law and regulations  -  Exclusion Criteria:  Patients meeting any of the following exclusion criteria are not to be enrolled in the study:  Patients receiving systemic treatment with strong or moderate CYP3A inhibitors or inducers within 14 days or five half-life times whichever the less prior to the first dose of study drug (refer to Section 5.2 for a list of example medications). Diagnosis of another concurrent primary malignancy.  Clinically significant cardiovascular disease, including any of the following:  Myocardial infarction or unstable angina within 6 months of study entry. History of or presence of heart block, and/or clinically significant ventricular or atrial arrhythmias. Uncontrolled hypertension defined as persistent elevation of systolic and/or diastolic blood pressures to ≥95th percentile based on age, sex, and height percentiles despite appropriate antihypertensive management. Planned non-protocol chemotherapy, radiation therapy, another investigational agent, or immunotherapy while patient is on study treatment. Any illness that affects gastrointestinal absorption. Ongoing or active systemic infection, active seropositive HIV, or known active hepatitis B or C infection. Any pre-existing condition or illness that, in the opinion of the investigator or sponsor, would compromise patient safety or interfere with the evaluation of the safety or efficacy of brigatinib. Patients with a history of cerebrovascular ischemia/hemorrhage with residual deficits are not eligible (patients with a history of cerebrovascular ischemia/hemorrhage remain eligible provided all neurologic deficits have resolved). Uncontrolled seizure disorder (patients with seizure disorders that do not require antiepileptic drugs, or are well controlled with stable doses of antiepileptic drugs are eligible).