∙ Part A - single-agent dose-escalation:

∙ \- Patients with histologically confirmed solid tumors or NHL. Patients with tumors known to be positive for deoxyribonucleic acid damage repair (DDR) defects (such as ataxia-telangiectasia mutated \[ATM\] deleterious mutation or low ATM expression) can be included.

∙ J-arm of Part A - single-agent dose-escalation in Japanese:

∙ \- Japanese patients with histologically confirmed solid tumors. Patients with tumors known to be positive for DDR defects (such as ATM deleterious mutation or low ATM expression) can be included.

∙ Part A.1 - single-agent dose-escalation with alternative dosing schedule:

∙ \- Patients with histologically confirmed solid tumors or NHL known to be positive for ATM loss and/or ATM deleterious mutations will be included. The biomarker status of patients in Part A.1 will be evaluated before general screening and only patients with the presence of the putative biomarkers of DDR deficiency will be recruited into general screening.

∙ Part B - single-agent expansion:

• Patients with DDR deficiency biomarker-positive advanced solid tumors of the following histologies: i) CRPC; ii) HER2-negative BC that is hormone-receptor positive (estrogen-receptor positive, progesterone-receptor positive, or both) or TNBC; iii) CRC, and iv) gynecological tumors (ovarian, primary peritoneal, and fallopian tube cancers, endometrial cancer, or cervical cancer).

• Patients with histologically confirmed advanced solid cancer, regardless of the cancer type, or NHL and loss of ATM protein by IHC.

• The biomarker status of patients in Part B will be evaluated before general screening and only patients with the presence of the putative biomarkers of DDR deficiency will be recruited into general screening.

∙ Part A.1 And Part B:

∙ \- Patients must be able to provide either samples of archival tumor tissue not older than 6 months or a fresh tumor biopsy during general screening.

∙ Part B.1 - single-agent expansion with alternative dosing schedule:

∙ \- Patients with histologically confirmed R/R MCL. These patients do not undergo biomarker testing to determine eligibility. The provision of baseline tumor tissue (archival or fresh) is strongly encouraged. If archival tissue ≤ 6 months old is unavailable, a fresh baseline biopsy may be obtained if safe and feasible.

∙ The following inclusion criteria apply to ALL (dose-escalation and expansion) patients:

• Patients with tumors resistant or refractory to standard treatment and in which, in the opinion of the investigator, experimental treatment with BAY1895344 may be of benefit. Furthermore, no standard therapy would confer clinical benefit to the patient. Patients in the MCL cohort of Part B.1 are to be relapsed or refractory to standard treatments.

• Patients must have measurable disease (as per Response Evaluation Criteria in Solid Tumors, version 1.1 \[RECIST 1.1\] or the Lugano classification as applicable, with the exception of prostate cancer patients who must have measurable or evaluable disease per the recommendations of the Prostate Cancer Clinical Trial Working Group 3 \[PCWG3\]).

• Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. For MCL patients: ECOG of 0 to 2.

• Patients must have adequate bone marrow function as assessed by the following laboratory tests to be conducted within 7 (+2) days before the first dose of study drug. Note that the below values are to be independent of red blood cell transfusions or granulocytes colony-stimulating factor (G-CSF) (i.e., no red blood cell or platelets transfusion within 28 days prior to the screening complete blood count \[CBC\] result, or administration of G-CSF is to occur within 14 days prior to the CBC result). Requirements for MCL patients are indicated below.

‣ a. Hemoglobin ≥ 9 g/dL. Patients with chronic erythropoietin treatment consistent with institutional guidelines can be included. For MCL patients: ≥ 8 g/dL; red blood cell transfusions during the screening period are allowed, and patients with chronic erythropoietin treatment consistent with institutional guidelines can be included

⁃ b. Absolute neutrophil count (ANC) ≥ 1.5 X 10\^9/L (≥ 1500/mm\^3). For MCL patients: ANC ≥ 1.0 X 10\^9/L. Patients with ANC ≤ 1.0 X 10\^9/L due to marrow infiltration may receive G-CSF during screening to bring pretreatment ANC levels to ≥ 1.0 X 10\^9/L

⁃ c. Platelet count ≥ 100 X 10\^9/L (≥100,000/mm\^3). For MCL patients: ≥ 75 X 10\^9/L